When we go to PF/Gatlinburg area, we LOVE Pine Mtn RV Park in PF, but we also have young (10 and 7) kids that like the pools (indoor and outdoor).
We have also enjoyed Smoky Bear in Cosby (further out, great campground with great reviews, but sites are smallish). Also Misty Mountain in Wallen, TN is pretty decent.
Lots of people like Riverside in Sevierville, but I find that it is a nice, but has a "snooty" feeling to me. It is right in the middle of all the traffic, but down over a hill, so you don't get a lot of noise, but getting in/out is almost impossible.
We have stayed at Elkmont and while it is nice being in the mountains, the lack of services (water/electric), makes it a no-go for us. The fireflies there are amazing and if you haven't heard of them, look it up before you go. A one night stay is definitely worth it just to see them and not have to get a shuttle up on the mountain from downtown.