We like Fall Creek Falls State Park in Tennessee. There is a lot of hiking, biking, and swimming available, but it might be getting too cool for swimming. George Hole and the Cascades waterfall are great for swimming!
We also camped in Kentucky at the My Old Kentucky Home State Park. We enjoyed the area, but the sites are a bit small if you have a larger TT or RV. They did have some grass camping, but I am not sure if they were only for tents. We also stayed at Boonesborough State Park and found the sites to be level and decent. We camped in a pop up two years ago that we had rented, but we now have a 30 ft. TT.
2010 Ford F-150 Crew Cab
2015 Salem Hemisphere 263RL