There isn't much "backcountry" in Kentucky, Tennessee, the Carolinas, Alabama, and Georgia in my opinion. Maybe I've missed it. Tennessee and Kentucky particularly seem to have a paucity of public grass strips. You might find some private folks with cool grass strips. These aren't "off the map" places but here are some of my favorites in the region:
Kentucky -- Even though they call it the Bluegrass State they don't have a lot of grass or backcountry-type flying that I've found. I did recently go to and recommend Middlesboro (1A6). Take the courtesy car and go to Cumberland Gap.
Tennessee -- Tullahoma has a nice grass strip and the Beech museum is there. I also like the Chilhowee Gliderport northeast of Chattanooga. Been a few years since I've been there but Sarah is an accomplished glider pilot and a fan of taildraggers.
Georgia -- check out Peach State Aerodrome (GA2). Good restaurant and a cool airport vibe.
Carolinas -- Ocracoke Island in the Outer Banks is a great spot with a spectacular beach. You have to get there by boat or plane so it's quiet. My wife and I went there a few years ago and she's still talking about it. If you're in that area, Tangier Island in the Chesapeake Bay is also an interesting day trip. Also interesting is the area known as the Highlands, around the town of Highlands and Cashiers NC. I've flown into Macon County (1A5) when I've gone there.
Alabama -- Moontown north of Huntsville (3M5) is a don't-miss type of place. I've been intrigued by Dauphin Island (4R9) but haven't been there.
Texas -- Terlingua out in Big Bend is a cool spot, especially if you're into dark skies. Cedar Mills (3T0) has a cool grass strip and a resort.
Here are some others I like:
Rainelle, West Virginia (WV30) -- this is a grass strip on top of a ridge. It's an airpark so there are people around. It gets soft in the winter; I went in April this year and one of the residents told me that the strip had just firmed up enough to land on and I was the first non-resident to land there this year. There used to be a restaurant there but it's long closed.
Natchitoches Louisiana (IER) -- apparently the oldest permanent settlement in the Louisiana Purchase; it has a cool downtown. I had a great stay there once and am overdue for a return visit.
You didn't mention Arkansas but there's some great flying in Arkansas. Check out Trigger Gap, Richland Creek (my favorite), Byrd's Adventure Center, and Gaston's (very well-known resort with a good Sunday brunch). Pine Bluff has a good airport restaurant if you're passing through. Bentonville (VBT) is sort of a hive for the area with a restaurant and an FBO that caters to the backcountry crowd. Their website is
https://www.flyoz.com.
Hope this helps! If I think of any others I'll let you know.