Dumplin Valley CG is a good suggestion. There is also a Bass Pro and minor league baseball stadium (a nice one too) around the corner.
In Townsend, we like Big Meadow which is adjacent to a rafting company as well.
But know that these are both regular CGs with rows of sites. Not with the isolated sites like it seems you are looking for. For that, state/national parks is where you'll have to go. I'm local if you want to PM me.
eta: whatever you do, stay away from Sevierville/pigeon forge unless you like fighting traffic and crowds.