This is an old list, but these are some of the open gyms that I used to frequent...
Aizah Volleyball
I haven't updated the list in a while because I moved to the city and no longer make the trip to the suburbs, but it should get you started. Chances are that all the towns have a park district and you can contact their park district to find out their schedules.
In the city, there's the
Chicago Sport and Social Scrubs... I mean Club
The other fairly large group in the city is
Player's Sports.