Chicago's live music scene remains super strong/awesome. It's one of the top reasons why I can never envision moving away from here. There are really too many possibilities to even directly answer your question. If you are a jazz lover, you've got Jazz Showcase and Green Mill, both incredible joints in their own way. I've heard good things about Winter's Jazz Club too, but haven't checked it out yet. Andy's on Hubbard is still around too.

Thalia Hall and Salt Shed are two relatively newer options that get a great variety of bands. They are pretty awesome. Metro, Lincoln Hall, Schuba's, Martyrs', Reggie's, The Hideout, Subterranean, and Phyllis' Musical Inn all continue to persevere and thrive as far as I can tell. Newer and arguably hipper options like Sleeping Village have come onto the scene as well.

Blues took a little bit of a hit when B.L.U.E.S. on Halsted closed, but you've still got Rosa's, Buddy Guy's, Blue Chicago, and Kingston Mines.  

Bigger venues like the Aragon, Riviera, Vic, and Park West are still chugging along too. You've even got two of my favorite places out in near-west suburbia where I live -- Fitzgerald's (the happiest place on earth if anyone asks me) in Berwyn, and Robert's Westside (brand new cool little venue) in Forest Park.

And there are plenty that I've missed. you really can't go wrong...enjoy!

Martyrs’
Reggies
Schubas
Chop Shop
Concord Music Hall
Bottom Lounge
Lincoln Hall
Park West
Empty Bottle