The Meriwether Lewis campground outside Hohenwald, TN is beautiful. (Meriwether Lewis died here under mysterious circumstances.There is a monument to him nearby.) Two sections. No hookups, no noise. We've never seen more than a few other campers there (sometimes no one but us). There is a small restroom building near the site for the seasonal host, but no shower. It is free.
If you have some time, get off the parkway for the day and visit nearby Hohenwald. It's a pretty, friendly little town. Home to the Elephant Sanctuary (elephants.com), the Lewis County Museum, a number of antique stores, and some surprisingly good restaurants for such a small town. Junkyard Dog for lunch or dinner, The Emporium (run by a church group, in a whimsically decorated old store) for lunch (great homemade soups, salads, and their own version of "cubans"), and the General is the local place for breakfast.
There's a SuperWalMart if you need camping supplies, grocery stores, at least two auto parts stores, and some cute little shops for fun.