If you're looking for a peaceful area then I would hit Townsend, TN as your base. Quiet little town. We enjoy staying at Big Meadow Family Campground. The Little Arrow Outdoor resort looks really good and the KOA doesn't look bad. Townsend is right at the entrance to the National Park, near the Cades Cove area. Lots of great hiking trails around there such as Abrams Falls and Rich Mountain Loop. Nice visitor center as well. Also convenient to the rest of the park. Heading to the North Carolina side is a beautiful drive and brings you past Clingman's Dome, the highest point in the park.
Townsend is an easy drive the Pigeon Forge and Gatlinburg if you're looking for some of that as well.