Look in the Townsend area. Called the quiet side of the Smokies. Close to the park and good restaurants in the area. The best part is a lot less traffic. Easy to make a day trip into the crazy in Pigeon Forge and then bail out back to peace and quiet.
Another option is Anchor Down in Dandridge. There is Panther Creek state park in Morristown. We like that when we can't travel far away from home. 9 full hookups so check early to see if available. Like someone else said, it's leaf looking time so it will be busy.
We also like the Maggie Valley area. A few nice campgrounds there too and fairly quiet at that time.