New Orleans is not the city it was, but you would hardly know it, wandering around the French Quarter on a sunny morning. The place has the sleepy grandeur of a colonial capital in Central America. Beyond the levee by Jackson Square, the Mississippi looks flat and peaceable. The St Charles streetcar rattles back and forth. Outside Café du Monde, the tables are full of people drinking its chicory coffee and eating plates of beignets, its signature deep-fried doughnuts, which threaten to embalm the eater in a layer of powdered sugar.
An early, grim-faced reveller clutches a beer and claims to be on the hunt for "a titty bar". I share his slightly manic eagerness to prove to myself that everything has returned to normal after Hurricane Katrina, so I order a vast plate of creole specialities in a restaurant – gumbo, jambalaya, shrimp creole, red beans and rice – stuff my face and totter out.
True, some shops seemed to be closed or closing. There are For Sale signs above some pretty French Quarter houses. But the French Quarter – which the French themselves called the Vieux Carré after Louisiana was sold to America – seems bigger and more beautiful than expected.
I was afraid it would be a beer-sticky creole Disneyland, but there are nooks to explore, extraordinary lace-iron balconies to marvel at, and beignet sugar to be removed from my eyebrows.
I start to think that maybe Katrina has already been survived and assimilated into the story of the city. On Bourbon Street, alongside the voodoo paraphernalia, there are photo books of the disaster for sale and T-shirts with slogans making light of it: "I drove my chevy to the levee and the levee was gone", "Make levee not war" and "I stayed in New Orleans for Hurricane Katrina and all I got was this lousy T-shirt, a new Cadillac and a plasma screen TV".
With typical American savvy, they've added the hurricane sites to the tours of the city. I pile on to a bus to see what Katrina has done to the place. We drive through the Garden District, where the city's 19th-century shipping elite built huge houses. At one time, this was the wealthiest city in America. The streets are shaded with jungly oaks, resurrection moss growing on their trunks. The gardens are heady with magnolias, azaleas, camellias, roses. The houses are extraordinary: fantasies in wood, with turrets, walkways, stained glass. Some still have slave quarters attached. Houses are being repaired where roofs were sheared off by the hurricane, but an old people's home has been abandoned. Some houses still show tide marks from the flood, up to three feet high in places. Yet the sense is of a district that has weathered the episode.
Much of New Orleans is below sea level. The original city was considered an island by the French. But in the swamp that surrounded it there were higher ridges; the rich had the smarts to build mainly on this safer ground. But when we drive to the Lower Ninth Ward between Claiborne and Florida, we see one of the worst-hit areas. Here, two-and-a-half years after Katrina, the scene is still one of biblical devastation. Whole tracts of land have been scoured of houses.
We drive in silence through the streets of wrecked neighbourhoods. The only sounds in the bus are audible gasps and cameras clicking. Many of the houses have been removed. Others stand a little askew on their original sites. Some were raised up off their foundations by the floodwaters and floated hundreds of yards. There's a vast lot of flooded police cars. We see ruined houses marked with painted band-aids by their displaced owners, and stencils saying, "Roots run deep here." In a few places, new foundations have been laid, new houses – on much higher foundations – are going up, but the general impression is one of utter desolation.
The guide tells us that 12,000 people were displaced; incredibly, one-third of New Orleans' population has left the city and is unlikely to come back. The houses that remain are marked with dates and symbols, indicating when they were searched and how many bodies were retrieved. Many of them are marked with multiple dates – the top floor was searched first, the lower floors a week or so later when the waters had receded.
Even the roofs tell a story – a pattern of missing shingles signifies the downdraft of a rescue helicopter; a neat exit-hole in the roof means rescuers cut out occupants trapped in the attic. Elsewhere, ragged punctures in the roof show where the most desperate smashed their way out from the inside. An old man sits by a makeshift memorial to the neighbourhood. Nearby a tombstone on a house commemorates two drowned children.
We get out to examine a house that has been broken open by the water. It's like something from a post-industrial Pompeii: a rusty microwave, boxes of earrings, crockery, a rack of shirts, CD players; everything warped, mouldy – but still recognisable as the remnants of a family home. The other tourists, all of them Americans, are clearly moved and indignant. "Fix the Ninth Ward, not Iraq!" demands some graffiti on one of the houses and there's an approving noise from someone behind me.
The land we are standing on is so low that you have to look uphill to the top of one of the levees that gave way. The water from the canal behind it poured onto the houses to a depth of almost seven metres, more than enough to inundate them entirely.
New Orleans is crossed by canals between the Mississippi in the south to Lake Pontchartrain in the north. During Katrina, a storm surge drove up the level in the lake and it poured back across the city, breaching the canal walls. As bad as the storm seemed, however, it has since emerged that the real culprit was the shoddy defences. After a long investigation u ointo the causes of the disaster, the head of the US Army Corps of Engineers admitted that the levees had been built to flawed specifications. Our guide tells us that this was the worst possible outcome. If the failures were due to poor workmanship, the levees could simply have been mended. It seems now that New Orleans' flood defences need to be entirely rethought. It's not clear when, if ever, the city can be considered safe.
I'm up early again the next morning to eat beignets and drink milky coffee under the ceiling fans of Café du Monde. There are two people hosing down the sidewalks of Jackson Square. I ask a shopowner why. "People urinate here," he says mildly. I suggest that maybe it's a good sign – people are back to their old ways, drinking too many cocktails as they head up Bourbon Street and this is the result. "Maybe," he says, "but they urinated here when things were pretty bad, too."
He shows me a satellite picture of the city after Katrina: 85 per cent of it is under water. There's a thin fringe in a lighter shade along the Mississippi that stayed dry.
I get different estimates of the economic damage from everyone I ask. The shop owner says business is down 40 per cent. At the Louisiana State Museum over the road, I'm told takings are down 70 per cent. The museum is eerily quiet and I am alone in a huge exhibition on Mardi Gras. There's something slightly distressing about the contrast between the energy and enthusiasm of the carnival exhibits and the big, silent rooms they're housed in.
Looking around the museum, it strikes me that Katrina is not so much a break with the city's history as of a piece with it. From the moment the French tried to settle here, it's been a continuous story of plans gone awry, disease, slavery, uprisings, fires, war, racial oppression, heat, and natural disasters. The museum plans a big exhibition on Katrina later this year. I hope that, in time, the hurricane will be another of the things that make up the story of the city, consolidating its sense of identity, but on my visit I find myself oscillating between gloom and hopefulness.
In an attempt to cheer myself up, I enrol myself in a Cajun cookery class. I want to learn how to make gumbo, the dark, muddy-looking soup that Louisianians use as a metaphor for the mixed heritage of their culture. It's a history lesson in a bowl: the base of onions, celery and peppers arrived with the French who founded the city in 1718 and wanted to make mirepoix but couldn't grow carrots in the swamp. It uses andouille, a twice-smoked sausage brought by German Catholics who came here later in the 18th century at the invitation of the French rulers. Its meats can be anything, but are influenced by the diet of the French-speaking Acadians – "Cajuns" – ejected from Nova Scotia in 1755 by the British. Displaced to the swamps of Louisiana, they raised chickens, and killed and ate anything furry or scaly they could lay their hands on: shrimp, crawfish, raccoon, coypu, rabbit, alligator. The soup can be thickened with okra from Africa, or ground sassafras leaves used by the native Americans. Finally, the spices and peppers which give the soup its kick are a legacy of the Spanish who ruled New Orleans from 1763 to 1801.
The toughest part of making gumbo, I discover, is having the courage to cook the oil and flour to the dark shade that gives the soup its authentic, swampy colour. This one was delicious, aromatic and sweet from the long sweating of the onions, peppers and celery – the holy trinity of New Orleans cuisine.
Almost nowhere can you escape the melancholy sense that the city is wounded. It's what everyone talks about. A taxi driver tells me his pre-Katrina fleet comprised 1,800 cars, now it's 1,000. An antique shop owner I chat to is selling up for good.
It feels like a terrible shame. There are cities that are bigger and more prosperous, but few that are so beautiful – still – and characterful, and with such a strong individual identity. What's more, through its music, New Orleans has shaped the lives of people who have barely given the place a second thought.
I walk north to Congo Square, now called Louis Armstrong Park. This is where, in the early 19th century, slaves would gather on their days off to play drums and strange stringed calabashes, ancestors of the banjo. White observers have left us rather snooty accounts of the weird atonal singing and lascivious dancing that went on here. After all, these are the earliest descriptions we have of the musical traditions that evolved into jazz.
But Armstrong Park is locked, and the French Quarter seems to grow more ramshackle and threatening as I reach North Rampart Street – the old border of the Vieux Carré.
The old French Quarter houses that face Congo Square are derelict, their once elegant windows boarded up. North of here lies what remains of Storyville, the district where, between 1897 and 1917, prostitution was made legal. Many of the whorehouses were cheap cribs, but the madams at the high-end ones spent fortunes on their decor and hired early jazz luminaries such as Jelly Roll Morton to entertain their clients.
I walk down to the Riverfront streetcar and take it to St Charles, where I pay 25 cents to transfer. I just miss the next one and end up chasing it down the street. Three times it stops and pulls away just as I reach the steps, waving my transfer ticket. I finally board it after running about a quarter of a mile, like a buffoon in a silent film. From streetcar level, things appear a little gloomier than they did yesterday. There's time to notice all the For Sale signs – I even spot an estate agent on the balcony of an elegant antebellum home, strangely unmistakable in his tie and crisp shirt, telling lies into his mobile phone.
I ride the streetcar all the way to the end of the line. This is South Carrollton, a leafy student area around Tulane University. I find the Maple Leaf, one of the city's stalwart live music venues. Next door is the restaurant Jacques-Imo's, heaving with customers, and painted inside to feel like a Cajun hut. Every Tuesday, the Rebirth Brass Band plays at the Maple Leaf, the first live music venue to reopen after Katrina.
The band don't start until 11pm so many of their fans come to Jacques-Imo's to eat first. As a lone diner, I'm whisked to my table ahead of the other punters. With misgivings, I order the shrimp and alligator-sausage cheesecake that the waiter recommends for a starter. It's delicious – like a sticky, cheesy, porky slice of polenta with sweet shrimps on it. Then, because I've always wanted to try them, I have fried green tomatoes: cooked in corn batter, spicy with cumin, and served with a sticky shrimp remoulade, which tastes like a Cajun prawn cocktail.
After dinner, I hang out with a crowd of people at Frenchy Galleries across the road from the Maple Leaf to kill time before the band come on. They're mostly long-term visitors to the city. Some have come to work as volunteers. In the aftermath of Katrina, there's been an upsurge in "voluntourism", people coming to New Orleans to help rebuild the city. Over in the Ninth Ward, I saw a street full of new pastel-coloured houses put up by volunteers from Habitat for Humanity.
Around 11pm, the Rebirth Brass Band begin setting up. They amble in unhurriedly. One of the trumpet players and a percussion guy don't arrive until the others are already playing. Rebirth has been going since the early Eighties, with a line-up that's constantly renewed from the pool of the city's musical talent. They face us like a firing squad, blasting their brass instruments until everyone inside is dancing. The music has real attack. There are tourists like me here, but also students, locals, friends of the band. In the corner, I spot one of the tourists who was on the tour of the Ninth Ward the day before. She's videoing the band and looks a lot happier than she did yesterday. The sound is loud and brassy and funky. The band feels like part of a living tradition, not New Orleans in aspic. It makes me feel hopeful that somehow, the city will find a way of renewing itself while staying connected to its traditions.
STATE LINES: Louisiana
Population 4.5 million
Area six times the size of Wales
Capital Baton Rouge
Date in Union 30 April 1812
Motto "Union, justice and confidence"
Nickname Pelican State
The writer travelled with Lastminute.com, which offers short breaks to New Orleans from £731 per person, including return flights from Heathrow with Northwest Airlines via Detroit, and three nights' room only accommodation at the Hotel Monteleone, departing in July.
There are no direct flights between the UK and New Orleans, but connecting flights are available with airlines such as Continental (0845 607 6760; www.continental.com), US Airways (0845 600 3300; www.usairways.com), United (0845 8444 777; www.unitedairlines.co.uk) and KLM/Northwest (08705 074074; www.klm.com) via their US hubs.
To reduce the impact on the environment, you can buy an "offset" through Abta's Reduce my Footprint initiative (020-7637 2444; www.reducemyfootprint.travel).
Hotel Monteleone, 214 Rue Royale, French Quarter (001 504 523 3341; www.hotelmonteleone.com).
Eating & drinking there
Café du Monde, 1039 Decatur Street (001 504 525 4544; www.cafedumonde.com).
Maple Leaf Bar, 8316 Oak Street (001 504 866 9359).
New Orleans School of Cooking, 524 St Louis Street (001 504 525 2665; www.neworleansschoolofcooking.com). Two and-a-half hour classes start at $27 (£14.20).
The Louisiana State Museum (001 504 568 6968; lsm.crt.state.la.us) in New Orleans comprises the Cabildo (600 St Peter Street); The Presbytere (751 Chartres Street), site of the Mardi Gras exhibition; the Old US Mint (400 Esplanade Avenue); the 1850 House (523 St Ann Street); and Madame John's Legacy (632 Dumaine Street).
All these sites open 9am-5pm daily except Monday, with the exception of the Old US Mint (10am-5pm daily except Monday, and until 8pm on Thursdays). Admission ranges from $3 to $6 (£1.60-£3.20).
Frenchy Galleries, 8311 Oak Street (001 407 758 5148; www.frenchylive.com).
New Orleans Convention and Visitors Bureau: 001 800 672 6124; www.neworleanscvb.com
Louisiana Tourism: www.louisianatravel.com