We stayed at Tishomingo State Park near Tishomingo, MS several years ago. It is close to Natchez Trace Parkway. The campsites were along a lake with plenty of "night sounds."
We also stayed at Piney Grove Campground, which is a few miles down the road from Tishomingo and also is close to the parkway. Piney Grove is a Core of Engineers campground on Bay Springs Lake on the Tennesee-Tom Bigby Waterway. We liked Piney Grove better than Tishomingo because Bay Springs Lake is much larger. We had a site right on the lake and enjoyed watching th bass boats zoom across the lake and also enjoyed watching the tow boats going up and down the Ten-Tom Waterway.