LBL has several good places, and the state of Kentucky also has a few CGs in the general area. I would recommend AVOIDING Lake Barkley State Resort Park on the east side of LBL, as it is somewhat run down, but Kenlake SRP (on the west side of LBL) and Kentucky Dam Village SRP (at the north end near the dams) are much nicer.
Inside LBL, the only CG I'm familiar with is Energy, but it is also pretty decent.
One thing you'll find with the CGs the farther south you go is all-but-nonexistent TV reception, but unless the weather is going to be bad, this is a minor complaint. (I personally like to be where I can watch a weather forecast!) Kentucky Dam Village is much closer to Paducah, so you'll be able to get all of the network stations over the air from that location.