I will 2nd or 3rd Pine Mountain RV Park in Pigeon Forge. We DO like Elkmont in the GSMNP, but it is dry camping and we just don't do that anymore. We have 2 daughters, 7 and 10. When we went to see the fireflies (if you don't know about them, google them) at Elkmont, we stayed 3 days and they were miserable. It was HOT, HUMID and WET. It didn't rain, but with all the humidity, water was just dripping the entire time.
We decided that the next time we go, which will be soon, we will get a site in Elkmont and put a tent there with a couple of chairs, but our RV will be sitting in PF hooked up to power and with the AC running.
Anyway, Pine Mtn is our favorite among the several dozen campgrounds we have tried in the area. Yes, Townsend, Cosby, Wallen and some of the other places are much quieter and 30 minutes out, but with kids, they want to be in town where the action is. It is a quick drive (less than 10 minutes) from Pine Mtn to the Sugarland welcome center and the entrance to GSMNP. Pine Mtn is also located on the "lower" end of PF, so you don't have to get in all the outlet traffic, but are right at the "kids" places, go karts, swings, etc. Pine Mtn has no playground, but they do have a pool and you have access to the hotel across the 2-lane road that has a lazy river pool, indoor pool and hot tub for those late night soaks.
We loved the Luray Jellystone when we stayed there a couple of years ago. I would recommend it if you have kids, but they enjoyed the campground so much, we never made it to the caverns.
You also might want to look at Natural Bridge SP in Kentucky, about 45 minutes SE of Lexington on the Mountain Parkway.
Also, the Ky Horse Park outside of Lexington is fabulous, but it has no sewer connections. If you are only going to be there a few days, it's well worth the trip and my kids LOVED seeing the horses and getting up close. There are numerous things to do in/around Lexington, which is about a 3 1/2 hr drive from the PF area.
If you do decide to go to Pine Mtn, PM me for some directions to avoid all the traffic on the bypass (Rt 66)