Adam, that's awesome! Like Charlie says, blues fest is May 29-June 1, maybe you can tell your boss that you'd rather not fly with the war on and delay until then? I'm a Chicagoland native and am trying to wrangle vacation time for that weekend. Are you staying in downtown, or going out to one of the 'burbs? If you're downtown, the clubs are easy to get to, out in the 'burbs presents a problem or two, but they're not insurmountable.
Unfortunately, I moved away before I was old enough to get into clubs all the time, but here's what I've found on my trips back over the last 7 years.
First, make sure that you catch Big Time Sarah and the BTS Express or Carl Weathersby if at all possible. They play regularly at the clubs around town and both put on incredible shows. (Both are also playing the blues fest, coincidentally).
Buddy Guy's Legends.
http://www.buddyguy.com/ Lots of the bigger regional acts & some national acts too. It's a pretty big place with a good stage, so they can cram a lot of people in there. Food's good too.
Blue Chicago
http://www.bluechicago.com/ Two sister clubs a block apart, pay the cover at one and get into both all night. One club is small and crowded, the other is larger and crowded. Mostly Chicago acts, I think, always good. Big Time Sarah is a regular here, as well as Willie Kent, and they're both great.
Rosa's Lounge
http://www.rosaslounge.com/ I've never been there, but it's highly recommended.
Kingston Mines
http://www.kingstonmines.com/ Another great venue. Great acts, great food, gets crowded quick. Tickets are getting pricey, though.
Fitzgerald's
http://www.fitzgeraldsnightclub.com/ In the very near SW suburbs (Berwyn), has a big variety of roots acts, a big stage, and a HUGE room. It's gotta be 25 yards from the stage to the back, and it's nearly a square room. Easy to get to from downtown by cab or public transport.
There's more, of course, but these are some of the biggies, and the only ones I've been able to find with web pages.