For a city so grand and so important – dominating America's vast heartland – Chicago is full of delightfully homey touches. Standing under the huge and beautiful Tiffany ceiling that was put in place 100 years ago in Chicago's biggest department store by Louis Tiffany himself, I asked a passing saleslady where most of her out-of-town visitors came from. Surely this glittering dome, one of the architectural gems of the city, would attract visitors from all over the United States, and possibly even Europe? The saleslady at Macy's, the new name for what was once the iconic Marshall Field's, thought for a moment. "I guess they're mostly from Grand Rapids, Michigan," she said.
Chicago is not a first stop on any grand tour of the States these days, but it should be. It is in many ways the city that defines the nation: Norman Mailer, who loved New York, was happy to call Chicago the last of the great American cities. It has everything an important metropolis should have – space, beautiful buildings and an astonishing history – plus a lively music scene and a lake so big, it looks like an ocean. It has a great deal of the energy and buzz of New York, but it's New York without the stress. Cars don't honk if you jaywalk, they slow down to let you pass. Nobody seems in too much of a hurry, which gives the city a midwestern feel. After all, it's on the tip of the Great Lakes and on top of the great grain-growing prairies.
At times, staring out from a window high above the city, it's possible to feel you're in the middle of nowhere. However, it was an architect friend's enthusiasm for Chicago's 20th-century buildings that drew me here originally – and I first came in the spring, when the ice on the rivers had melted and the soaring office towers gleamed in bright sunshine.
Chicago was born around 1800 in a stinking swamp: a fur-trading post with a fort and three taverns. Yet by 1837 it had incorporated itself into a town with a mayor. Planks were laid across the mud to make roads and move goods. By 1848 there was a rudimentary railway system and 10 years later Chicago had become the railroad hub of America, a status it still holds. Soon the city was also the greatest grain port and the largest lumber market in the world.
Immigrants, at first mostly Irish and German, swarmed in to take advantage of this unbridled capitalism, though many of them were to live in appalling conditions. By 1862 the city was the biggest meat-packing town anywhere, dealing with up to 200,000 hogs a year. (The smell of the butchering and the meat processing plants apparently rivalled the stink of the original village.) The jostling city was also to become the most corrupt and crime-ridden in the United States.
Then came the fire of 1871, when 17,000 buildings were destroyed and 100,000 people – one-third of the population – were made homeless. Everything changed again. Tall buildings began to go up, to house the homeless and give the landlords back their rent. Chicago has always claimed to have built America's first skyscrapers, and the city that had so much space to spread itself outwards preferred to renew itself upwards, which it continues to do today.
At the end of the 19th century, serious cultural activity arrived for the first time. Soon the Art Institute of Chicago was attracting more visitors than New York's Metropolitan Museum (and is still an essential 21st-century stop for the visitor hungry for culture), and the Auditorium Theater gave a proper home to the new Chicago Symphony Orchestra. In 1893, Chicago hosted a World's Fair, a huge event with 27 million visitors, including 10,000 African-Americans, many of them newly arrived in the city from the South. And with the new immigrants a different kind of music would soon emerge.
The black musicians who came upriver to Chicago made it the nation's premier city of jazz and blues. They congregated on a half-mile strip on State Street called "The Stroll", Louis Armstrong, Jelly Roll Morton and Kid Ory among them. In the South Side area you'll find some of the original jazz clubs, like the Green Mill, most of them open till four or five in the morning. Buddy Guy has his club, Legends, on South Wabash Avenue, a great cavern of a place where I found Mr Guy himself sitting at the bar happily signing programmes and his own branded T-shirts. Van Morrison, the Stones, Bo Diddley and the Pointer Sisters have all played gigs at the venue. My companions and I settled for a local bluegrass band, twanging happily away in the gloom while we nursed our cold beers and imagined ourselves back into the speakeasy days of the Prohibition era, which ended only a lifetime – 75 years – ago.
A short taxi ride away is Symphony Hall, now the Chicago Symphony's home, where the virtuoso trumpet player Wynton Marsalis is a regular performer with his Jazz at Lincoln Center Orchestra from New York. He is a brilliant communicator: I heard him give a lesson in the rudiments of rhythm and the genius of Count Basie to a rapt audience of local schoolchildren aged from six to 12.
If you're in Chicago on a Sunday morning it's also worth paying a visit to the House of Blues and its Gospel Brunch ("Praise the Lord and Pass the Biscuits!") down on North Dearborn, where before the show you will be offered a rib-sticking Southern-style breakfast of eggs, the ground corn dish called grits – white and sticky, hash browns, bacon, ham, shrimp, pancakes, muffins, what they call biscuits but which are more like soft savoury pastries, waffles, and strawberries and cream. After this feast I skipped food for the rest of the day, though you could work some of it off by going shopping. The "Magnificent Mile" – otherwise known as North Michigan Avenue – has more than 460 shops along its elegant edges, from big smart ones such as Neiman Marcus, Saks and Bloomingdale's, to the small.
Under instruction from my architect friend, I spent plenty of time in Chicago craning my neck: gazing up at the massive and wonderfully curlicued Wrigley Building, built in 1920, and at its neighbour the neo-Gothic Tribune Tower, put up in 1925, with its fantastical buttresses and gargoyles. These astonishing buildings stand side by side with ultra-modern creations and still manage to look at home: even next to Donald Trump's latest power statement, the 90-plus storey Trump Tower, still under construction. Trump's new building was planned to be the world's tallest, but after 9/11 its height was scaled down by several hundred feet to reduce its appeal as a target for terrorists. It will end up as Chicago's second-highest building after the Sears Tower.
Great clusters of soaring skyscrapers dot downtown Chicago, and its main avenues – unlike New York's – are wide enough for you to be able to stand back to admire them. Better still, go – as I did – on one of the Chicago Architecture Foundation's guided tours, which you can follow on foot, or from one of their special tour boats. From time to time on the river, massive barges swing across your bows, a reminder that these are still working waterways. Away from the river are fine examples from Chicago's adopted architectural sons – Frank Lloyd Wright's long, low Robie house, now almost 100 years old but newly restored, with beautifully decorated glass windows and Mies van der Rohe's equally breathtaking Illinois Institute of Technology, with its curtain walls of brick and glass, over which the roof seems almost to float.
You can combine the visual pleasures of modern Chicago with its traditional musical richness by visiting Frank Gehry's remarkable Pritzker pavilion, the outdoor auditorium in Grant Park. I loved the brushed stainless steel ribbons which billow out from the stage and connect to an overhead trellis of steel pipes. This supports a sound system which, I was told, successfully reproduces the acoustics of an indoor concert hall. In the summer months the Grant Park music festival gives hugely popular free classical music concerts – a tradition going back to the Depression days of the 1930s when few could afford to pay.
In the new Millennium Park one of the main attractions is British architect Anish Kapoor's enormous curved stainless steel structure, officially called Cloud Gate but which most locals affectionately refer to as "the bean". Its curved surface reflects and distorts the neighbouring high-rise buildings and the delighted spectators in a way that is both comical and beautiful.
But my favourite Chicago experience was on board one of the Tall Ships which you can find at Navy Pier. As we sailed sedately into the lake a mile from shore, rigging creaking gently above our heads, we avoided being press-ganged by a keen young skipper's mate into hoisting the mainsail and admired instead across the water the thrusting skyline of one of America's most astonishing cities. Though as Mark Twain once observed, "It is hopeless for the occasional visitor to try to keep up with Chicago – she outgrows his prophecies faster than he can make them. She is always a novelty, for she is never the Chicago you saw when you passed through the last time."
The writer travelled to Chicago with British Airways (0870 850 9850; www.ba.com), which flies from Heathrow. Virgin Atlantic (08705 747 747; www.virgin-atlantic.com), American Airlines (020-7365 0777; www.americanairlines.co.uk), United Airlines (08458 444 777; www.united.com) and Air India (020-8560 9996; www.airindia.com) also fly direct from Heathrow. American Airlines (020-7365 0777; www.americanairlines.co.uk) also flies from Manchester, as does BMI (0870 60 70 555; www.flybmi.com).
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).
Fairmont Hotel, 200 N Columbus Drive (001 312 565 8000; www.fairmont.com/chicago). Doubles from $287 (£151), room only.
Chicago Cultural Center, 78 E Washington Street (001 312 744 6630; www.chicagoculturalcenter.org). Open 8am-7pm Monday to Thursday, 8am-6pm Friday, 9am-6pm Saturday and 10am-6pm Sunday.
Art Institute of Chicago, 111 South Michigan Avenue (001 312 443 3600; www.artic.edu). Open weekdays 10.30am-5pm, until 8pm Thurs; $12 (£6.30).
Green Mill Jazz Club, 4802 North Broadway Street (001 773 878 5552; www.greenmilljazz.com).
Buddy Guy's Legends, 754 South Wabash (001 312 427 0333; www.buddyguys.com).
Symphony Hall, 220 South Michigan Avenue (001 312 294 3000; www.cso.org).
House of Blues, 329 North Dearborn (001 312 923 2000; www.hob.com).
Trump Tower, 330 North Wabash Avenue (001 312 644 0900; www.trumpchicago.com).
Grant Park Music Festival (001 312 742 7638; www.grantparkmusicfestival.com). This year's line up will be announced on 7 March.
Millennium Park, Downtown (001 312 742 1168; www.millenniumpark.org).
The Chicago Architecture Foundation's tours are based at the ArchiCenter, 224 South Michigan Avenue (001 312 922 3432; www.architecture.org).
Chicago Tourism Bureau: 001 312 567 8500; www.choosechicago.com
Illinois Bureau of Tourism: 001 800 406 6418; www.enjoyillinois.com