Townsend, TN is billed as "The Peaceful Side of the Smokies" and is about 20 minutes from Pigeon Forge if you take Wears Valley Rd (if you stay in Townsend I can give you more details on that, it's really easy).
http://tremontoutdoorresort.com/
Tremont is my favorite in Townsend, it's right outside the park entrance, is shady, has a pool and you can get a site right on the river. They don't have a very impressive website, which is a shame because the campground is nice.
If you stay in the park itself, none of the campgrounds have pools but you can swim in the creeks. We've visited all the park campgrounds and prefer Cades Cove Campground. Also, the park campgrounds don't have showers.
In Pigeon Forge itself, our oldest son stayed here and really enjoyed it.
http://www.foothillsrvparkandcabins.com/
They have shaded sites and a pool.
I could talk for hours about the area, like Disney, but I don't want to overwhelm you. If you have any questions feel free to ask. I'd be happy to answer them if I can.