I really don't know of any places near the airport.  However, both airports have links to our public transportation system that will get you downtown If you are coming from Midway, you take the Orange line train downtown.   If you are coming from O'Hare you take the Blue Line downtown.  Both around 45 minutes for just a few bucks. Andy's has food and jazz. Buddy Guy's Legends has food and blues. Jazz Showcase has drinks and jazz, but you will be amongst some of the best jazz artists on earth in a very intimate setting. There are many more places, but not in the downtown area.

Great taste in music, JayCross!  



Thanks for the feedback, Oneperday.  You know I love me some good blues & Jazz.

Hot chicks singing on the piano in saloon girl getup.  Very good food too!