Go for a high-flying city break in the Windy City crack
The numbers on the lift dial speed upwards: 65, 66, 67... and we're not even near the top yet. Willis Tower - formerly known as Sears - is not for the vertigo-prone, I swiftly realise as I take the ear-popping ride towards the heavens. Once the proud holder of world's tallest building status, it nestles these days between Chicago's legion of skyscrapers, a symbol of the sky-high aspirations behind it.
Slightly dizzy from my rapid ascent, I stumble into the viewing gallery and gasp. Far beneath me, a breathtaking panorama stretches out in three directions.
The fourth vista includes Lake Michigan, so vast it could easily be an ocean.
It is heady, to say the least, to look west and imagine the great American heartland rolling out beyond the horizon, hundreds of miles to the edge of the Pacific. But seeing it from above does not give you a feel for this breathtaking city.
For that, you have to go down to the streets, smell the burgers and fries, hear the blues in the bars, feel the sand of the lake shore beach between your toes.
However, despite boasting all these pleasures and more, Chicago is unfairly overlooked at times. It may be the self-styled "Second City" of the US, but compared to its flashier rivals it attracts far less publicity.
Los Angeles trades off its Hollywood glamour, San Francisco its hippy past and New York - well, it needs no epithet.
And Chicago? We can name deep-pan pizza and corrupt local government as two of its better known products.
But there is far more to it than this.
Unlike its supercool cousins, the city does not sit on the trendy East or West Coast, but in the rather less hip Midwest. This makes it something of an unexpected treasure when, after driving through the endless Illinois prairie land, its majestic skyscrapers appear on the horizon.
Built on the shore of Lake Michigan, it is a modern metropolis accommodating some of the finest architecture in the Western world. The best way to see this is by boat. To get my bearings, I take a Chicago Architecture Foundation cruise along the turquoise river that snakes through the heart of the city.
Towering overhead on both banks, against a piercing blue sky, are a dizzying number of Victorian, Modernist, neo-classical, neo-Gothic and Postmodernist masterpieces - all built since the Great Fire of 1871, which all but destroyed the centre. The blaze provided Chicago with an opportunity to start afresh and fashion a wonderfully liveable new city from the embers of the old.
European influences abound - as one tour guide told us, "America didn't have its own architectural style before Frank Lloyd Wright" – but Chicago looks nothing like anywhere in Europe.
Its triumphs include Tribune Tower, whose resemblance to a cathedral is not accidental - the home of the Chicago Tribune was inspired by Rouen Cathedral in Normandy, complete with decorative buttresses and scrollwork.
My favourite - The Carbide and Carbon Building is designed to look like a champagne bottle, with every bit as much fizz and sparkle in its unusual gold tower and dark green base.
And then there's the beach - a charmingly incongruous addition to the urban landscape.
Gaze out from it across the lake and you'll fancy yourself on a seaside holiday. Turn around and you'll see the skyscrapers looming over you – a surprising contrast. The pleasant walk along the lake shore - or cycle ride, if you prefer - will take you to touristy Navy Pier.
While Navy Pier merits a visit - especially for the twice-weekly firework display - it is not a place to spend the bulk of your time.
Chicago is not cheap, although plentiful meals that don't break the bank can be found if you look hard enough.
Manny's Deli is the best lunch option for those on a budget. A no-frills, canteen-style deli, it serves what could well be the best Jewish food this side of New York: chicken soup with matzo ball or kreplach, potato pancakes, kishke, herring... It's all there for you to pile up high on your plastic tray.
Chinatown is also relatively inexpensive and worth a visit - if only to window shop down the main drag, where restaurants and shops dish up exotic fare or peddle dust-covered junk.
In search of authentic American grub, I selected from the long list of steakhouses Harry Caray's, a smart and pricey eatery established by the eponymous baseball announcer.
Chicago is not a city that never sleeps. There's no lack of nightlife, but it does get its beauty sleep. Maybe that's why it feels so laid back and fresh.
After dark, if you squint, you can picture Gotham City. But open your eyes wide and you'll see the Midwest's finest jewel: a stunningly conceived slice of urban America.
Best for: Spectacular architecture and rich history.
Time to go: Early summer or early autumn, when the climate is moderate.
Don't miss: A river boat tour on the river is an ideal way to see the city.
Need to know: The CTA - Chicago's train system - is a good way to get around but taxis are also relatively cheap.
Don't forget: Save the diet for when you get home: burgers, chops and hot dogs are standard Chicago fare.
Return prices start from £368.70, including taxes and surcharges, from London Heathrow and from £370.90 ex-Manchester.