A.H.
Hi M.!
Well, you've already had someone mention Parents Who Care, although I'll just add my backing to that one. They've got an open gym during the winter and summer camp during the summer that are great to get the kids out playing with other kids! They also have a bunch of other awesome programs. Definitely worth checking out. Again, they are at http://www.parentswhocare.org .
Also, if you haven't checked out meetup.com for groups yet, there are some there as well. I'm in one that covers a really broad area range (http://sahm.meetup.com/99/), as well as one closer to me for Elgin and Cary (I'm in Carpentersville). You might search for more localized Schaumburg ones - there probably are some.
Welcome to the area!