Another thing to think about when visiting the city is HotTix. They are half price tickets available the day of the show. They have tickets available for most major producitons in Chicago and are not incredibly difficult to get ahold of. I know of two different booths. One is located on Michigan Ave in the old water tower.
Second City is great for improvisational sketch comedy.
They have a world wide reputation for the greatest comedic actors and actresses. They have daily shows and free imporv sets that are every night after the show except Friday. This is not stand-up, if you want that go to Zaney's. The Annoyance Theatre has a great show that has been running for a very long time. It's not for the weak stomached though.