I had mentioned the Palatine YMCA, which has the indoor play maze but I have found out since that you have to be a member to use it!
I just found a few more places for you to try:
Lake Zurich (gymnastics center with open gym times):
http://www.usgtclz.com/og.htm
Barrington (gymnastics center with open gym times):
http://www.kiaga.com/pages/2/index.htm
Lake Zurich (Ela area Library has a play area and some good programs, sometimes drop-in):
http://www.eapl.org/
If you have 15 1/2 month old son, say...then here are some places to check out! ;o) (If this is who I think it is?!)
Arlington heights:
http://www.littlevillageplayplace.com/index.htm
Mundelein:
http://www.pretendplayground.com/
Elk Grove Village:
http://www.elkgroveparks.org/pavilion.asp?id=222
If this is not close enough than ask for a specific location and someone might know of other places. You should also pick up an Oaklee's Guide from your local library. Your local Library may also have free storytimes for tots which end with a little open playtime. You can also check out local Parenting groups through the guide online: http://www.oakleesguide.com/parenting.htm
I hope some of this helps.