Oxbow Park in Byron is a great family place. Huge picnic area, zoo, hiking trails, fishing, camping and almost all of it is free.
There is also Chester Woods camping area. Again, hiking, fishing, boating, swimming, biking, camping and there is even an orienteering by GPS set up there. But this is a State Park, so you will need to purchase the state park sticker.
Whitewater State Park is just outside of St. Charles. A lot of varied activities there as well. Again a State Park so stickers are required.