You didn't say what your preferences are. Most of the best suggestions (Chicago Reader) already taken, but if you're into Irish music/culture there's an Irish American newspaper available at the numerous Irish import shops that lists concerts and other live music, etc. Also depending when you're there there are a bunch of Irish festival in the area all summer long.
If you want culture there's the Field museum and Oriental Institie at the U of C, also the Aquarium.
Have fun, the food and music is great!