Clinton Lake State Park has plenty of camping spaces (over 400) so you won't have to worry about finding a spot. The sites are nice because there are plenty of trees and plenty of ground to spread out your tents. If you have an RV or camper, the gravel is big enough to accommodate your vehicle. You aren't far from the hiking trails or the lake. My camping party happens to be rowdy, but we've had no problems with rangers or bothering others around us.
Clinton Lake has over 30 miles of hiking and horse-back riding trails and 9,000 acres of public hunting land. There's plenty of fishing opportunities too.