This is Soldier Field right ahead of us," says chirpy tour guide Britney, rocking back on her Segway to stop and explain the history of Chicago's South Side sports stadium. But her words fade out of earshot as I glide away from the group – Segway whirring, my orange plastic poncho billowing out behind me – towards a small metal cabin on the pavement. What's the lure? Kim and Carlo's: one of the city's renowned hot-dog stalls. The smoky, savoury smell draws me in like catnip.
The Chicago hot dog is the stuff of food legend. Like the city's soaring skyline – a confluence of neo-classical, postmodern, art deco and prairie-style architecture that takes your breath away – it's perfectly constructed, made to a strict formula with a Vienna Beef wiener shrouded by fresh garnishes and hot yellow mustard. Ketchup is forbidden. Within seconds, I'm biting through a soft, poppy seed-flecked bun, into the rich beef dog, my senses blasted by the mustard, crunchy onion, sweet relish, celery salt and astringent dill pickle. It's the perfect fuel for someone who's been using rather a lot of energy trying not to fall off a Segway.
At the turn of the 20th century, Chicago was the US meat-packing hub, the industry employing more than 25,000 people and producing 82 per cent of the meat consumed in the States. This meaty heritage, coupled with the city's varied immigrant communities – Italians, Austrians, Poles and Germans flocked here to find work – means that Chicago has long been known for this kind of down-to-earth folk food. The deep-dish pizza was born here, and the crispy stuffed-crust sausage pizza pie at the graffiti-strewn Gino's East is a comforting lunchtime treat, its crust barely able to contain the molten cheesy contents. You'll see a queue winding around the block for space in this buzzy, scruffy place; diners scrawl their names on any available surface.
The city is also revered for its steakhouses. That night, I feast on perfectly charred, butter-tender bone-in fillet at Gibsons steakhouse in the Gold Coast district, which sources beef from a farm in Minnesota, where the cows are "grass-fed and corn-finished" and the meat is aged for 40 days – all of which gives it an incredible depth of flavour. Any visit to Gibsons should begin with one of the expertly crafted martinis available in the bustling bar downstairs, and end at Blue Chicago, where local blues acts are best enjoyed accompanied by the deliciously fruity Honker's Ale – a malty craft beer from the nearby Goose Island Brewery.
Yes, it all sounds like a recipe for a giant food hangover. Luckily I'm staying at what US Health magazine has dubbed "America's healthiest hotel", the plush Peninsula in the swanky Near North Side area of the city. The top floor of the hotel is dedicated to health and fitness, and you can offset some of the damage done with treatments in the outstanding Espa spa, swim in its 25m indoor pool, or take in the views of Lake Michigan from the floor-to-ceiling windows of its gym while you pound the treadmill. But I'd be lying if I told you it was the gym that had attracted me here. The hotel has four restaurants, including The Lobby, whose sous-chef, Mario Morales, takes me on a tour of Lincoln Park's fantastic Green City Market.
Mario quickly finds inspiration for his menu in the heaving tables of local produce, plucking heirloom beets from Michigan that he later fashions into wafer-thin ravioli and fills with delectable Wisconsin cheese. We wander through the leafy bazaar, past everything from elk meat to maple-candied pecan ice cream.
"The market was started by the late food writer Abby Mandel, who was inspired by the French markets and wanted a similar thing for Chicago – a way for people to connect with local producers," Mario says as we walk. "It started out on a very small scale in an alley downtown, but had to move here in 2000 because it was growing so fast." Now, the market receives 300,000 visitors a year and is considered a model for markets nationwide.
More recently, it's been Chicago's pioneering gastronomic chefs who've catapulted the city to global culinary fame. In 2010, it joined New York and San Francisco as the only American cities with annual Michelin Guides. I visit Alinea, which last year achieved the ultimate accolade of three stars. It's an unassuming grey-brick-fronted building in the city's Lincoln Park district.
"In the last five years, the city has really exploded in culinary terms," says Grant Achatz, Alinea's auburn-haired chef. "You have Alinea, Charlie Trotter's, L20 – Michelin two- and three-starred restaurants – but then you have amazing taco places, Thai food and everything in between."
In the food world, 37-year-old Achatz – who overcame tongue cancer, which left him temporarily unable to taste – is known for his influential modernist American cuisine. At Alinea, patrons don't eat the tasting menu's intricately crafted 22 courses from plates, but from specially designed tableware which has been crafted specifically to deliver certain menu items. I taste his lauded "Hot Potato, Cold Potato" dish – a cold truffle and potato soup served in a shallow wax shell, pierced by a pin threaded with morsels of butter, Parmesan, chive, hot potato and black truffle.
Achatz instructs me to pull the pin "like a grenade" – dropping its elements into the soup. It's a thrilling amalgam of textures and temperatures: the earthy depths of truffle and potato lifted by the Parmesan and chive – refined yet deeply comforting. Then comes a beignet of pheasant, apple jelly and roasted shallot, sprouting a cluster of oak leaves, which he sets on fire with a blowtorch, filling the room with an evocative autumnal smell. It's revelatory.
As is my meal at the chef's new restaurant, Next, which opened last year in the edgy Fulton Market meat-packing neighbourhood, a stone's throw from the avant-garde Moto, where futurist chef Homaro Cantu dishes up baked-bean spaghetti and edible menus. Next is a bustling, brasserie-style restaurant but, as you might imagine, there's a twist: every three months, the style of cuisine changes completely, and diners buy tickets for their meals before the night they dine. On my visit the theme is "Contemporary Thailand". I devour squidgy-sweet roasted baby bananas with crispy fried garlic and coriander flowers, then braised-beef cheek curry with peanut and lemongrass.
I'm impressed. And so was Ferran Adria, the Spanish godfather of molecular cuisine, whose recent visit to Next resulted in his collaborating with Achatz on an elBulli menu that runs until March, showcasing 20 dishes from 20 years of his now-defunct elBulli restaurant. Transferring elBulli from the balmy beauty of the Mediterranean to the gritty Midwest? Having eaten my way around it, I'm starting to realise that in Chicago's food scene, anything is possible.
The writer travelled with British Airways (0844 493 0758; ba.com), which offers three nights' room-only accommodation at The Peninsula Chicago from £829 per person, including return flights from Heathrow. Chicago is also served by United Airlines (0845 8444 777; unitedairlines.co.uk) from Heathrow and American Airlines (020 7365 0777; americanairlines.co.uk) from Manchester.
The Peninsula Chicago (001 312 337 2888; peninsula.com) has doubles from $560 (£366), room only.
Chicago Segway (001 312 552 5100; chicagosegway. com). Two-hour Segway tours cost $60 (£39).
Kim and Carlo's (kimandcarlos chicagostyle.com).
Gino's East (001 312 988 4200; ginoseast.com).
Gibsons (001 312 266 8999; gibsons steakhouse.com).
Blue Chicago (001 312 661 0100; bluechicago.com).
Alinea (001 312 867 0110; alinea-restaurant.com).
Next (001 312 226 0858; next restaurant.com).
Moto Restaurant (001 312 491 0058; motorestaurant.com).
Chicago Tourism: choosechicago.com