The KOA and Jellystone are both gross. The KOA might as well be in the median of the interstate. We drove through last year when we stayed at Jellystone and marked it off the list for good. Jellystone is slightly better. Sites are super tight and not hardly a shade tree to be found. There is however alot of stuff for the kids to do including free putt putt, giant jumping pillow, pool, waterslide, and fishing pond. Mammoth Cave itself is neat but after one tour we were pretty much done. Diamond Caverns is a good tour if you are in the area as well.
Nolin Lake State Park is the nicest campground in the area in my opinion, pretty small but sites are waterside and huge. No full hookup though.
You could check out Natural Bridge State Park which is in the Red River Gorge area. Lots of hiking, and pretty scenery.
Breaks Interstate Park is beautiful, but not alot to do in the area. Its on the border of Virginia and KY.
We go to Townsend every year and its our favorite. I have alot of other suggestions if you want. We are from KY if you want more suggestions.