Winnebago County does a great job of maintaining their Forest preserves and campgrounds. They charge a fee for non-residents, but it's worth it. Not spectacular, but very pleasant and relaxing. Sites are open, but well spaced. Plenty of shade. Hike-in sites are on the riverbank, about 200 yards from parking.
 The Sugar river is scenic, and easy to paddle up or down, so you can do round trips without having to arrange drop-offs. 
The Pecatonica river is nearby as well. A good day trip is Monroe, Wisconsin, home of the National Cheese Museum and Alp & Dell Chees works, a great place to shop for chees lovers. Van Eyck Orchard is a great stop as well.