Sure you're familiar with Blue Chicago, Kingston Mines, and B.L.U.E.S. but there are other venue in Chicago that also offer Blues. Below is a list of not so well known venues that also have the Blues.
Fitzgerald's - Bluesday Tuesday
6615 Roosevelt Rd, Berwyn IL
Fitzgeralds offers a wide array of different music genres every month. Check they're calendar for more info.
1200 W Randolph,Chicago(West Loop)
City Winery offers an intimate space to see Blues events and enjoy food and different types of wine.Check they're calendar for more info.
CITY WINERY CALENDAR
2105 S State Street Chicago (South Loop)
Reggies offers a wide array of music genres including the Blues. Check they're calendar for more info.