Tennessee Valley Authority (TVA) maintains some excellent campgrounds and recreations areas on the rivers and lakes near their dams. They are very well maintained and patrolled by the TVA police. A map is here:
TVA: Dams and Power Plants
Click on the little squares to get the name of the dam and then click on that to go to a page with more info on the area. Down at the bottom of the info page is a link to camping facilities available there. Most have showers and picnic areas, often with electricity. At some you can reserve a campsite in advance.
Tennessee also has excellent state parks, many allow camping.
TN State Parks: Find A Park: Camping
There are also lots of private campgrounds around.