Gino's Pizza is a tourist favorite since it's one of the better deep dish pizzas in the city. But if you're in for a good pizza place that's not touristy, take the Red Line up north to a place called Pequod's (you can find directions by public transit on google maps). After you're done eating you can walk around the Lincoln Park area, which is really nice. It'll be cold, so dress warmly!
Another thing you can do is head to the Chicago Architecture Foundation and take a tour around the downtown portion of the city. I'm not 100% positive they do winter tours, but it's worth investigating.
Another fun thing to do is go up either the Sears Tower or the Hancock Building. Of the two, people say the Hancock has the better view. Neither is free, but the Sears is about $15 to go up, and the Hancock is actually a bar/restaurant. So if you spend $10-$12, you get a drink and a view.
Millennium Park is pretty great, if it's not too cold, and so is the Art Institute, if you like art.
The Chicago Cultural Center is a nice free destination if you're in the downtown area; especially if you're headed to Millennium Park or the Art Institute.
I'd also recommend checking out the Field Museum, Shedd Aquarium, and/or the Museum of Science of Industry (more out of the way, but very cool).
Hope that helps!