We spent a week's vacation in KY last summer & stayed at these 2 CG's that I would recommend (both w/fhu):
Cave Country RV Campground
. Big-rig friendly & close to Mammoth Cave.
. Small, family-owned campground with beautiful stream sites. Choose the perimeter sites which are roomier & well-shaded (some have wood patios), as opposed to the pull-thrus which are tighter & out in the open...unless, of course, you need clear overhead for satellite reception.
I've got reviews of both CG's w/photos on the website's Campgrounds section (if they ever get it up & running). In the meantime, you can check out my photos of those CG's on the website's Photos section - listed under my member name, pages 4-6.
If you're not opposed to KOA's, the Corbin KOA
gets consistent high marks on rvparkreview's website. Although we haven't stayed there, we have scoped it out & it has sites set amongst tall trees & a new section of deluxe pull-thru's with stamped patios & patio furniture. A bit pricey, but quite comfortable sites for extended stays.