If you are into Boutique gear then definitely Bass Club Chicago (
http://bassclubchicago.com/2010/index.php). They have all the insane boutique basses you never thought you could ever try, like Ritter, Modulous, Fodera, etc. I was there a few weeks ago and actually got to try a Ritter!! They also stock Bergantonio cabs which are really difficult to try out without ordering one.
If however, you are into vintage stuff then go to Chicago Music Exchange (
http://www.chicagomusicexchange.com/). They have a crazy amount of guitars/basses there. Lots of vintage fender, plus lots of Ricks and Stingrays. Also have a few vintange SVTs from the 70s/60s.
Both places have "sound-resistant" rooms for you to try gear out in.
Also have fun at Buddy Guy, he is awesome live.