We like River Plantation in Sevierville but it is a commercial type campground. Read the reviews and zoom in on Google Maps earth view to see details. You might check into Townsend and drive into the park. The KOA in Townsend probably has more for kids to do. There is a Jellystone Campground in Cosby TN about 30 minutes from entrance to the park.
In Sweetwater TN is Lost Sea Cavern. Walk down and then boat ride.
In WV: Cass Scenic RR in Cass WV is neat.
New River Gorge Bridge is nice to visit. Near there is Lake Summerville Corps of Engineers park. No sewer at site but dump station.
We liked Luray KOA in Luray VA but not sure the caverns would be good for very small children. (read reviews).
