When we went to LBL, we stayed at Energy Lake, it is very nice, we also drove through a few of the others, all were nice. You will find that most of the campgrounds have spacious sites, some have more trees than others, and shade can be important in TN and KY in the summer.
One of the things that we did was to drive down to Fort Donelson, I was indifferent before we went, but my husband really wanted to go, so we did, our son, the husband and I. We got to the information center, and were told that there was a presentation happening in 5 minutes at a site about a mile down the road. We rushed down there, and found that it was just us and the ranger, who treated the three of us to an hour plus long fantastic accounting of the history of the Fort, I was so glad that we went. We then wandered through the buildings and looked at all the artifacts and old pictures. Definitely recommend the trip for history buffs.