Jazz Showcase, Winters, Andy’s or the Green Mill - just check on line for the line up and take your pick. Jazz Showcase is a fair sized room/club, Winter’s is a small intimate listening room (no chatting during performance), Andy’s is pretty much an open bar (serves food) and can be noisy so beware of where you sit, have never been to the Green Mill but it is a hike from downtown.
The absolute best is the jazz series at the Chicago Symphony Center, they bring in main line talent for a series every year, check the schedule to see if it matches your visit, cso.org