Chicago doesn't really have a huge central market like some other cities (e.g. Seattle's Pike Place Market). The two places I would suggest visiting are the French Market ( www.frenchmarketchicago.com ), which is a brand new market that recently opened in one of the commuter train stations just west of the Loop, and Fox & Obel ( www.fox-obel.com ), which is an upscale gourmet grocery store just northeast of the Loop, with the finest quality meats, fish, prepared foods, etc. Both are places where you can grab lunch. Don't miss the cinnamon swirl rolls at F&O.
Other than those, though, many Chicagoans shop at a variety of stops, especially when looking for the best of everything - one market for produce, another for cheese, a butcher for meats, etc.
I think the one "can't miss" specialty in Chicago is our Chicago-style deep-dish pizza. There are a lot of places serving great pizza here, and the chains (with the exception of non-downtown locations of Uno's) do quite a good job of maintaining consistent quality across many locations. Take your pick - single-crust "pan" pizza from Lou Malnati's, Pizano's, Gino's East, or the original location of Uno or Due, or double-crust "stuffed" pizza from Giordano's, Edwardo's, or Bacino's - you can't go wrong with any of these. The original locations of Uno and Due in River North started it out in 1943, and are as good as any place. You can phone your order ahead of time if you want to avoid waiting 30-45 minutes while seated for your pizza to bake; you can find their menus and locations on their websites:
At the high end, some of the best restaurants in the entire country are here - very expensive ($200-300+ per person including moderate wine/alcohol and tax/tip), dressy (jackets required for gentlemen), and wonderful, offering an unforgettable experience:
1. Alinea - Grant Achatz - Lincoln Park - www.alinearestaurant.com
2. Everest - Jean Joho - Loop - www.everestrestaurant.com
3. Charlie Trotter's - Charlie Trotter - Lincoln Park - www.charlietrotter.com/restaurant
4. Avenues - Curtis Duffy - Michigan Avenue/Streeterville - http://chicago.peninsula.com
5. TRU - Rick Tramonto - Michigan Avenue/Streeterville - www.trurestaurant.com
6. Spiaggia - Tony Mantuano - Michigan Avenue/Streeterville - www.spiaggiarestaurant.com
We also have some wonderful contemporary American, casual fine dining restaurants. IMHO the very best ones are:
North Pond, in addition to having wonderful food, has an exquisite setting, too. It's right in the middle of Lincoln Park (the park, not the neighborhood), on the pond (the building used to be the place where people would rent ice skates in winter), with the city skyline as a backdrop at the opposite end of the pond. It's about three miles north of downtown, an easy cab or bus ride ( www.transitchicago.com ).
And, we have some excellent Mexican restaurants. Before you start thinking, "Oh, we have those at home", please realize that these feature very creative provincial Mexican cuisine. Take a look at the menus on their websites and you'll see what I mean. Frontera Grill and Topolobampo ( www.rickbayless.com/restaurants ) are in River North, and others close by include Salpicon ( www.salpicon.com ) and Mexique ( www.mexiquechicago.com ).
A local "don't miss" snack is Garrett's for caramel popcorn and cheese popcorn, with several locations in the Loop. www.garrettpopcorn.com
There are lots more places, particularly in outlying neighborhoods where you find more ethnic places (Thai, Indian, etc) but they involve some traveling from downtown (30-60 minutes via public transportation).
So those would be my first recommendations. You can find more detailed discussions about specific types of food here in these other topics:
Brunch and Breakfast:
Bottom line, if you're in town for the weekend, I think you could go to Uno or Due for pizza for lunch one day, hit Cafe des Architectes or North Pond (or Alinea!) for one dinner, have another dinner at Frontera Grill/Topolobampo or Cafe Spiaggia, do Sunday brunch at David Burke's Primehouse, stop in at Fox and Obel and at Garrett's, and you'll be having some of our best eats.
Feel free to ask more questions. Enjoy your visit!