We have found a campground that gets very little use, and tends to be very quiet.
If you want someplace to just sit and relax (Not a whole lot else going on.), Old Stone Fort state park is a pretty quiet place. There is a short hiking trail arround the "Stone Fort" which sits within the "Y" of 2 rivers. An old Indian stronghold, you wouldn't even know it was there if you didn't know what you were looking for. Other than that, there is a golf course down the road, but no pools or beaches, etc. We like it because it is usually only at about 50% capacity, even on the weekends, and very quiet.
WARNING: Watch out for "Bonaroo" weekend! It's a once a year modern day Woodstock type festival. You won't want to be here during that! From what I understand, you won't want to be within 50 miles!
I like this one, too. It's nice to camp among trees and have a decent sized site.