The colors will still change whether or not the park is still open. There are many roads across the southern part of the Appalachians, and many RV parks open.
But from western Tennessee, for fall colors I would go into the forests of the Ouachita Mountains in SW Arkansas and SE Oklahoma, or anywhere in the forests that remain in the Ozark Plateau (southern Missouri, or NE Arkansas to actually find the Ozark Mountains).
Our I would drive around in the forests of western Tennessee, western Kentucky, southern Indiana. Not everything has been cut down and farmed.
You need to get the timing right. E.G. no point in coming to SW Arkansas, SE Oklahoma in two weeks, because you will be too early for color. Still green, temps in the mid-80s here, fall comes here in late October to late November.
Timing is why I'm suggesting where you are, and further north. I just got back from southern Michigan, and colors were just starting to come out, in a small way, last week.