So.. I asked a few coaches, and I got the following recommendations:
IN the city:
Peterson Park District
Chicago Park District
Outside the City:
Elk Grove Gymnastics (I like this gym, but it's a bit older and smaller. However, I frequent it a LOT)
Aurora has a few clubs...
In reality, it comes down to what you like, and what you expect and like in a club atmosphere. If you want a really nice gym to work out in, Wilmette Park District has a wonderful gym... other than that.. find someone who you gel with, and stick with them!
Good luck! I hope to hear good things about a new gymnast in town :-D
Ryan