In the back....
Fenton Lake Access Recreation Area is pretty awesome. Off Ky68 in Land Between The Lakes, Kentucky/Tennessee.
First there's the campground, which is not phenomenal but gets the job done. Located in the back to the left, the sites run along a hillside. There is a pit style toilet on site and dumpster. The road continues into the woods along the back side of the bike trail. At the very back before turning around ( don't drive on the bike trail) is an open area which would support a large group and there are trees large enough for a tree tent and hammocks.
At the campground entrance there is a pavilion area good for a large gathering. And like I already mentioned there is a bike trail that continues through the area from cement back onto dirt track also nice for hiking.