Another vote for Brantley Lake State Park. Quite nice and very quiet. ;)
If you arrive after dark, you'll feel like you're driving an eternity off the highway on a 2-lane blacktop to nowhere.... It's 5 miles off the road.
We went this past February. Elevators are NOT working in the caverns... You must hike back UP the entire thing... Tentative date to have them turned back on is May 31. https://www.nps.gov/cave/planyourvisit/conditions.htm