We liked Lowden State Park - pretty simple, electric-only sites, but nice and wooded and lots of cool birds. The park was near the campsites so we could keep an eye on the kids. Nice short hike to the look-out area by the river (the Indian statue is still wrapped, last I heard). Not much privacy between sites.
The Jellystone in Millbrook is great for kid activities, but kind of pricey. The reason we like it is simply it's not too far from home and has a heated shower-house open year round. Great for fall trips. Although I imagine it's a giant ruckus in the summer.
We also spent a night at Chain O Lakes up north. That was a pretty basic campground, electric only sites, a decent shower house and pit toilets spread around. Nice trees. Not a whole of privacy. The loop we were in had basically no activity or excitement, which was a little boring. But cheap!
Wisconsin Dells area has good stuff. We stayed at Baraboo Hills with 3 other families last Labor Day and had a great time. Definitely crammed in, but lots of stuff for the kids. The drive up was terrible (we're coming from southwest suburbs and it was Labor Day weekend, in fairness). Honestly I would not go back just because of the drive. There are other similar private campgrounds much closer to home.
We are looking forward to our first trip on Memorial weekend at Rock Cut State Park, so I can report back on that one soon!
We go to Condit's Ranch in Putnam, Illinois. About 1.5 hours down 80 from Orland Park. We like it. Friendly place. Rustic enough to feel like camping. Family atmosphere. Usually have bands or karoake on the weekends.
Thompson Causeway in Thompson, Il - Nice facilities on Missisippi river. Beautiful.
Middle Fork Forest Preserver Penfield, IL - Nice sites, in the country, fishing and hiking.
Morraine View State Park near Leroy (Bloomington) - Nice lake, swimming available in summer, fishing and canoeing
Comlara park north of Bloomington - Very nice lake, good sites and facilities
Illini State park (Marseilles) - Close to Starved Rock, some nice sites on the IL river, or more wooded in other areas.
Turkey Run in Indiana - Awesome park. Can be hard to reserve
Devil's Lake Wisconsin - Awesome park. VERY hard to get reservation
Kettle Moraine Wisconsin (multiple CGs) Lots to do; fishing, swimming, hiking, decent availability if you can deal with non-electric sites.