A friend and I went to Prentice Cooper State Forest once and it was fun. A lot of mild, wooded trails. I've since found out there may be some stuff we didn't get to there that's just a bit more challenging but should still be fine for a stockish vehicle. I wish I'd known about Coppinger when we were there. I'd like to try it as well.I've heard ( from @AndyG ) that coppinger cove rd, in sequachie tn, is perfect for stockish jeeps. I've been wanting to check it out for a while.
And the service roads at land between the lakes are pretty fun, and mostly mild off roading.
https://www.tn.gov/agriculture/forests/state-forests/prentice-cooper.html