I've been in middle TN for almost 18 years now. There are very few other places I'd rather live. I live in Lebanon, just a little East of Nashville. TN goes through the typical four seasons. The late Summers can be hot and humid, but the Spring and Fall are great and the Winters are fairly mild. Middle TN can be hilly is areas. The further East you go, the more hilly it becomes. The Eastern part of TN is home to the Smoky Mountain National Park. From Nashville, you can be there in under 4 hrs. Great place for hiking and camping. Plus the state parks, like Fall Creek Falls, are great places as well.
Deer hunting in Tn is pretty good. There's a good bit of public land spread through out the state. Some public areas get hunted fairly hard but, with a little effort, finding a decent place to hunt isn't hard. I take deer every year off public land. The deer herd is estimated to be 900,000 plus head. In the Eastern Middle and Eastern part of the state, feral hogs/boar are in good enough populations for decent hunting. If you like black bear hunting, the Eastern counties have good populations and established hunting seasons for them. We have a growing elk herd up on the Cumberland plateau. There's been talks of a limited special tag elk hunt sometime in the near future, but nothing definate.
There are a couple of traditional clubs in the state. The Old Fartes are around Crossville and the Lost Tribe is closer to Memphis. Recently, a state traditional orgainzation has formed,
http://ttaswnl.site.with.us/home . From what I've heard, the clubs home range is probably going to be at Henry Horton state park. That's a little South of Columbia, not too far from Franklin. Then there's Twin Oaks up around Clarksville. Not a traditional only club, but they have a strong traditional membership. They hold a big 3 day, traditional only shoot every Spring. It's a great shoot.
If you decided to move this way for certain, drop me line and let me know you're coming. I'd be happy to help you get settled in.