I'll also add a big recommendation for Townsend. We've been there many times and always enjoy it. We stayed at
Big Meadows Family Campground and really liked it.
In September we are going to try
Little Arrow Campground. That is recently rebuilt and has new owners. Looks really nice.
In any case, Townsend is nice and quiet, near the National Park (especially the Cades Cove area), and a short scenic drive away from Pigeon Forge and Gatlinburg.
Big Meadows is probably the most "parking lot" like followed by Little Arrow. The KOA has a lot of trees and looks nice.