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 city panorama stretches out in three directions.

The fourth vista includes Lake Michigan, so vast it could easily be an ocean.

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.

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 goverment as two of its better known products.

But there is far more to it than this. 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. A sort of Midwestern Xanadu perhaps.

My favourite, The Carbide and Carbon Building, is designed to look like a champagne bottle. And then there's the beach — a charmingly incongruous addition to the urban landscape.

The pleasant walk along the lake shore, or cycle ride, if you prefer, will take you to touristy Navy Pier. While meriting a visit, especially for the twice-weekly firework display, it is not a place to spend the bulk of your time.

I lingered longer in the Art Institute of Chicago. A whole day, in fact. With one of the best collections of Impressionist paintings in the world, this enormous gallery is an art lover's paradise.

Also worth a look is the American Modern Art section, where Grant Wood's American Gothic hangs alongside works by Edward Hopper, Georgia O'Keeffe and others.

Conceptual art-filled Millennium Park offers a vast expanse of green on which to lay back and take in that skyscraper-lined skyline some more.

The park will give your purse a rest as well. No, 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.

At the end of each day, I collapsed into my queen-sized bed at Hotel Indigo — a plush and pristine boutique hotel in the Gold Coast neighbourhood, perfectly situated for sightseeing on foot.

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 — with Coke and extra fries.

To help plan a holiday in Chicago, visit www.visit chicago.com