When visiting relatives in Knoxville, we stayed at the Misty River RV Park in Walland, about 15 mins south-west of the city:
Misty River Cabins & RV Campground
It's situated close to the Smokey Mountains Park, Pigeon Forge and all the touristy stuff and yet is in a lovely grassy area close to a river and, despite being quite close to a fairly busy road, was very quiet when we were there.
We don't often stay in commercial campgrounds but would definitely go back to Misty River; a cleaner and better run campground you'd be hard pressed to find.
*** After posting edit ***
I've just looked at the website and it looks to me as if the place has changed hands. There used to be a ton of information and videos available but now it's largely about Townsend Cabins and very little about the campground. Hopefully it'll be as it was but you never know