I loooooove Chicago, it's my favorite US city! Definitely do the art institute, especially if you like paintings. I'd also recommend the Architecture Foundation's riverboat tour, it's a great way to see the city and learn it's history. You can take a tour of the old city library, which is now the cultural center, it's a beautiful art deco building, and the tour is really detailed. Milennium Park I'd say is also a must-see.
For restaurants, try Lou Malnati's for the best Chicago-style pizza, and there's a great little place called Crofton-on-Wells that has a nice romantic atmosphere and great food. I also like Topolobampo because it's outside-the-ordinary Mexican, and Harry Caray's for the atmosphere--if you go to an afternoon Cubs game, go there for dinner that night.