B.Z.
Try www.oakleesguide.com for some ideas around the suburbs. There are coupons in there, and several of the events cost money, too. But occasionally there is a great concert or festival that is free!
You live close to Cosley Zoo and Klein Creek Farm... both are free. Just bundle up before you go.
We spend some time at the malls and Cabela's when it's too cold to be outside or when there are no other events. Cabela's is near I-90 and Rt. 59, and it has a lot of stuffed animals (stuffed as in taxidermy).
Lastly, check with your library and park district and the ones in surrounding towns. Usually you will have to sign up ahead of time, but the events are frequently free. You can get the Museum Discovery Pass from your library if your library participates.
Have fun!
Editted to add: Cantigny Park has free admission on patriotic holidays. It is very affordable during the weekends if you wanted to bring a carload of friends on a sunny day. There is a museum and beautiful grounds for walking around. You can see tanks on the property and read the history while the kiddos climb on them.