Chicago has some fantastic museums! I would check out The Field Museum and then the Science And Industry museum. If you're into art The Art Institute of Chicago is the place to go. While you're there do check out Portillo's! Some of the best Italian beefs and Chicago hot dogs I have ever had! But there are many good eats there, you can't go wrong. They feed you right in Chicago. Try a Chicago pizza!
I was born in Arlington Heights and have family in Chicago. I haven't been there in seven years.
U2 is a good band. I have the War and Joshua Tree albums. Use to listen to Bloody Sunday and New Years Day all the time while playing Goldeneye with my Bro on the N64.
Did you hear Bono messed his arm up?
THese are good recs. Science and Industry is on the other side of town, though (Hyde Park), so you'd have to train + bus, or cab it to get there. It's pretty good though. It's mostly aimed at kids, but it's pretty good for "old kids" as well.
The Art Institute is world class. Tough to pass it up when you are in town.
Shedd Aquarium is also in that area, so you could Art Institute/Shedd/Natural History/Millenium Park all in one rather busy day, without walking too far.