If your going to Chicago, the last thing you'll have to worry about is finding something to do! Some good suggestions of info sites : Look up the Chicago Reader online - it has info re: the literally hundreds of plays going on, all the music you could desire, cultural events, museums, etc.
As well, the weather is usually nice come May (although you never know - there were snow flurries in June at the lake about 7 years ago in the beginning of June) and a visit to the Lakefront can be a day long trip!
Other good music venues:
Schuba's on Southport & Belmont for wide variety Kingston Mines, Blues Chicago anf Blues ETC. for Blues
Enjoy your visit!