We all know how much Frank Sinatra yearned for the big city, but what about the place he left behind? Andrew Spooner finds elegance among the booze, broads and casinos

Frank Sinatra was always too big for Hoboken. You can hear it in the way he sang "Start spreading the news, I'm leaving today" in "New York, New York" – pure, unbridled joy. The sophisticates of New York have always derided Hoboken, the little town at the wrong end of the Holland tunnel whose blues Frank was so eager to shake off. Even Bugs Bunny agrees. "Hoboken?" he wails in one cartoon, "Ooooohhhhh, I'm dying again!!"

Frank Sinatra was always too big for Hoboken. You can hear it in the way he sang "Start spreading the news, I'm leaving today" in "New York, New York" – pure, unbridled joy. The sophisticates of New York have always derided Hoboken, the little town at the wrong end of the Holland tunnel whose blues Frank was so eager to shake off. Even Bugs Bunny agrees. "Hoboken?" he wails in one cartoon, "Ooooohhhhh, I'm dying again!!"

Hoboken is only a $1.50, 15-minute train ride from downtown Manhattan and is as close to Wall Street as Central Park. It is, however, in New Jersey, which for New Yorkers is purgatory. But once I heard that Frank was born and raised there, I knew I had to leave the bright lights and pay homage.

Hoboken's biggest problem is that most visitors, like Frank, turn their backs on the place. They mostly come here for one reason – to stand and stare at Manhattan. Directly across the Hudson River, the views from Hoboken of the skyline are awesome. However, I want to give Hoboken itself a little more attention, as I'm on a search for traces of Frank. My first destination is 415 Munroe Street – the legend's birthplace.

Exploring Hoboken is easy enough with its familiar grid structure. The main drag is Washington Street, a run of bars, nightclubs and fancy shops. "On Saturday nights Washington Street is one endless mookathon," explains Jim, my Hoboken-residing pal. (A "mook", for the uninitiated, is an Italian-American colloquialism, which roughly translates as "yobbo".)

The Italian and, supposedly, mob connection is legendary in this part of New Jersey. I keep expecting Carmela Soprano to come strolling out of one of Washington Street's glitzier shops laden with purchases. David Anthony, a local politician, tells me it's all a put-on. "There's no gangsters here," he says with a wink. "Well, at least, they don't show up on my radar."

Most of the Italian community used to work in Hoboken's once thriving port. These days, the dockers' neighbourhoods have been replaced by gentrified, brownstone workers' cottages and clapboard housing. Eventually, I arrive at Munroe and Sinatra's birthplace. I am expecting some kind of celebratory marker, but somewhat disappointingly there is nothing more than a small, star-shaped plaque on the street. I want to complain, but who would listen?

Before I leave town, I head for Hoboken's legendary pizzeria, Benny Tudino's. "You have to go to Tudino's," Jim explains. "It serves the biggest slice you've ever seen." He ain't wrong. Tudino's serves up an enormous slab of oozing cheese and pungent pepperoni on a delicate, crispy base. The best thing, as with all American pizza, is that you get to eat it with your hands.

Disappointed with Hoboken's apparent lack of interest in Frank, the next morning I set off down the New Jersey Parkway towards Atlantic City, the place where Frank first saw his name in lights. Atlantic City is as rich in history as it is in casinos. The legends of mobsters, corruption, vice and colourful Vaudevillian entertainment have meshed together over the years to create an American epic.

Founded in the mid-19th century as a seaside health resort, by one Dr Jonathan Pitney, Atlantic City quickly became the premier leisure spot for the East Coast's masses. However, they did not come for the bracing sea air. As Murray Fredericks, a 1920s hotel owner, once explained: "They wanted booze, broads and gambling, so that's what we gave 'em."

Added to this were freak shows and fairgrounds with their boxing cats and diving horses. The world's first wooden boardwalk was built here, and piers and music halls flourished. Frank was discovered on the Steel Pier in the 1930s, singing with Henry James's big band. The urban working classes of Philadelphia, Washington DC, Baltimore, New Jersey and New York came in their millions to lap it all up, and under the increasingly influential Mafia bosses, organised crime gathered momentum in the background.

I arrive in the lobby of the Caesar's Palace Resort and Casino with a smile on my face. In the corner stands a huge, faux-Roman statue of Julius Caesar, encircled by numerous, equally faux, classical columns. Hundreds of elderly, overweight, badly dressed Americans are milling around. An endless chorus of bells, hoots and clinking coins emanates from an enormous bunker filled with brightly lit fruit machines.

To get to my room I have to pass blackjack tables, spinning roulette wheels and cocktail waitresses dressed in tacky mini-skirts. Most of the punters don't seem to engage with their surroundings but simply loll, empty eyes staring at the rotating coloured drums of the slot machines. I climb a short run of stairs and get a full, astonishing view of the place. The casino floor is gargantuan, almost twice the size of a football pitch, with endless rows of people pecking at the machines like battery chickens.

I'm not a gambler but I do have a cunning, if flawed, plan. It includes visiting one of the psychics on the boardwalk to get the skinny on my chances. Then, I'll take my paltry budget, stick it on the right numbers and become a rich man. But first I need to get some lunch.

To Angelo's diner in Duck Town, the city's old Italian neighbourhood. I'm wondering what the special is. "We got the veal and peppers over spaghetti," the waitress barks. Sounds tasty. But not as tasty as the table full of sharp-suited geezers who are sitting around the next table. And they say there's no Mob in Atlantic City these days ... I feel like I'm inside a living cliché. Photographs of Frankie Avalon, Rocky Marciano, Joe Di Maggio and Robert De Niro adorn the walls. Sinatra – I'm pleased to report – is providing the soundtrack, and red gingham covers the tables. What brings it all together is that one of the suited gentlemen is wearing loafers with no socks – on a snowy February afternoon.

I walk off lunch with a stroll along the boardwalk. I pass the gaudy, architectural excess of Donald Trump's Taj Mahal – think Brighton Pavilion meets too much money. I keep going until I reach Tina and Cher's $1 psychic readings. A pretty young woman appears from a back room. She takes my palm and fixes me with her bright blue eyes. "You ain't been feeling too well lately," she drawls, "and you're gonna feel better soon. That's your reading." I had hoped for something a little more incisive. Oh well. You gets what you pays for, I suppose.

I head back to Caesars, my master plan shredded. I decide I'm going to play the slots and break a $5 bill into quarters and dimes. But confusion quickly subdues my enthusiasm. These American-style fruit machines are a complicated array of video pictures, buttons and levers. In one section of the casino, I even stumble upon slots that cost an incredible $1,000 a spin. Eventually, I find rows of generic one-arm bandits that suit my simple tastes. I slip my first quarter into the slot. "Keeerrrrrchiiiinnggg," and I've won with my first attempt! My winnings total 50c – two quarters – doubling my bet. Do I get out now while I'm still ahead? I decide to carry on. Every few spins, the machine spits a small amount of money back out at me. It's just enough to keep me interested and believing that soon I'll win big. As Sam "Ace" Rothstein says in Scorsese's Casino: "The golden rule is to keep them playing. The more they play, the more they lose. In the end we get it all."

They don't get it all but they do get $50 of my hard-earned cash by the time I drag myself away. I feel like I've been in the casino for about 30 minutes, but a quick glance at my watch reveals I've been stuck in this windowless bunker for five hours. Money and time are precious commodities and I'm being drained of both. However, my casino encounter does reaffirm something that had been clear to me from the start: I'm no gambler. And, if you don't gamble, there's little reason to be in Atlantic City. So, I decide to leave the Sinatra legacy behind and move an hour further down the New Jersey shore for something altogether more genteel.

My destination is Cape May, the US's first purpose-built resort town. First stop, though, is the nearby seaside town of Wildwood, home to the finest collection of Doo Wop architecture in the whole country. I wondered the same as you – what the hell is "Doo Wop" architecture? Luckily help is at hand in the form of Wildwood's Doo Wop Museum and Joanne Galloway of the Doo Wop Preservation League. "It's all about movement and action," she says. "In Wildwood we have dozens of authentic 1950s motels. They were fashioned in an era of rock 'n' roll and bobby-soxers and they convey the optimism of that time. The name Doo Wop (also an a capella musical style of the 1950s) was chosen as it evokes the playful spirit of the age."

We jump in a car for an impromptu tour. The motels are the epitome of cool modernity, with sleek lines, bright colours, heavily garnished with chrome and neon. Names such as the Caribbean, Tahiti and Rio abound and each is themed according to an inferred location. Every motel proudly displays plastic palm trees, celebrating kitsch and irony, while out front the funky signage is pure Americana.

I peek inside the 20-room Starlux Motel. Built in 2000, the Starlux is a multi-million-dollar contemporary retro-take on the 1950s theme. The open-plan lobby has blue-glass walls and butterfly chairs while the bedrooms are trimmed with aluminium. The effect is a sleek, shimmering grooviness finished off with a fabulous kidney-shaped pool. Unfortunately, I don't have time to spend a night at the Starlux: I'm heading 10 miles down the coast to Cape May.

If Wildwood is about movement then Cape May is all about stasis. Everything here is focused on preserving a 19th-century ambience of refined gentility. Arriving at the handsome Queen Victoria b&b, I am offered a high tea of cakes and perfectly cut sandwiches. I sit down to eat in a suitably grand leather armchair, meditating on a large log fire. Soothed and rested, I take a short walk around Cape May's leafy environs. Row after row of wonderfully preserved Munsters-style houses fill the streets (the ghoulish TV family was supposedly resident in New Jersey, trivia fans). They are painted in bright pinks and blues with turrets and balconies, American Gothic style. Each lawn is beautifully manicured, every picket fence is a brilliant white.

That night, lying in my comfortable four-poster bed at the Queen Victoria, I reflect on my journey. I have visited New York many times before and had always adopted the city's snooty attitude to New Jersey. What I have discovered is a thriving homage to Americana that includes pizza, mobsters, Sinatra and the finest lodgings. On my next visit, however, I will be certain not to gamble.

The Facts

Getting there

Continental Airlines (0800 77 6464; www.continental.com) flies direct to Newark, New Jersey, from Glasgow, Birmingham, Manchester and London Gatwick. Return fares start from London start from £247 in May.

Being there

Double rooms at Caesars Palace (001 888 241 8545; www.parkplace.com) in Atlantic City start from around $142 (£94) per double per night, including all taxes, but excluding breakfast.

Angelo's, 2300 Fairmont Avenue (001 609 344 2439).

The Starlux Motel (001 609 522 7412; www.thestarlux.com ), 305 E Rio Grande Avenue, Wildwood, offers doubles from $77 (£55) on a room-only basis.

The Doo Wop Museum (001 609 523 2400; www.doowopusa.org), 3201 Pacific Avenue, has a definitive collection of Doo Wop signage and other memorabilia. From 24 June, you can also take a Doo Wop 50s trolley tour around Wildwood. Tickets cost from $8 (£5.30). Call for details (001 800 275 4278).

The historic Queen Victoria Bed & Breakfast Inn (001 609 884 8702; www.queenvictoria.com), 102 Ocean Street, Cape May, offers doubles in May and June from around $137 (£98) including breakfast and afternoon tea.

Benny Tudinos, 622 Washington Street (001 201 792 4132).

Frank Sinatra's birthplace can be found at 415 Munroe Street.

Further information

New Jersey Tourism (001 609 292 2470; www.visitnj.org).