My answer on Facebook that was popular...
I grew up in Chicago, from a family that loved to eat out, and a lover of meats and fatty foods (not for the health conscious, but you're visiting Chicago, right?). First, if you're visiting Chicago, you have to eat steak. It was the historic hub of the cattle industry, Morton's Steakhouse was founded here, and where else are 48 oz portershouses standard?
The local favorites are The Chop House and Gibson's. You can't go wrong with either, but Chop House has been rated "best steakhouse" in America for several years by numerous publications so I would go here. After growing up on Chop House, Gibson's, and others, Peter Lugar in Brooklyn was weak. "Steak for three" at Lugar's is like a steak for one in most Chicago steakhouses.
For higher end restaurants, I would recommend Alinea, Charlie Trotters and MK Restaurant. Alinea and Moto started the micro-dish trend (20 course dinners) several years back and frequent experimentations with liquid nitrogen.
For mid-tier priced restaurants and street food, there are countless choices. If you can travel out to the burbs, I would recommend Bob Chinn's Crabhouse in Wheeling, IL. This is one of the best seafood places you'll ever eat at and has the best Alaskan King Crab (yes, in the burbs of Chicago). They have their own daily shipments of fresh seafood flow in and the largest volume of King Crab. This one restaurant generates over $30 million in revenue and typically ranks 4th in the nation. In Chicago, I would recommend going to Rick Bayless' Frontera Grill. Bayless was the winner of Top Chef Masters last year and is an excellent chef.
For fast food, I would recommend Portillo's (chain with many locations) or Al's Beef and get the Italian Beef sandwich. If you haven't tried Italian Beef, then you haven't been to Chicago. Get it "dipped" (in beef juice) with peppers. Then travel to Buffalo Joe's in Evanston, IL and go to Buffalo Joe's. Their buffalo wings have won two national recipes (for any food) and is the standard for many wing fanatics. Their consistency in quality and size of the wings have gone down over the past decade, but it's still tasty.
Then find a Pot Belly's for one of the best subs you'll have. This was a Chicago institution for years with only two locations until several years ago Starbuck's Howard Schultz invested into it and expanded it throughout the Midwest and D.C.
For pizza, Giordano's is my favorite. It's stuffed pizza, not pan so it's even thicker and heavier with meats and cheese. Voted "Best Pizza in America" by NBC and others. I would also check out Spacca Napoli if you love Neapolitan style. And a local favorite in the burbs is Burt's Place, which has a pretty good fan following.
Update 1/9/2011: Recent TIME magazine article on Grant Achatz and Alinea, a three star Michelin restaurant
The hottest restaurant in Chicago right now is Girl & the Goat, which was started by Top Chef winner, Stephanie Izard