My experience, based on 30 years of living in Tennessee, is that there is not a lot of good public deer hunting in Tennessee. It is not because there aren't public lands to hunt, but because almost everyone in Tennessee deer hunts. So, you can drive to the public hunting area at 3 in the morning, and cars will be stacked up everywhere and the woods full of people. I'm not just talking about rifle season, I'm talking about bow season too. (Late season muzzleloading is a little better, but not much.)
The Land Between the Lakes Wildlife Reserve, the Cherokee National Forest, and Hatchie Wildlife Refuge are all within driving distance of Nashville. There is also a big state park, in south central Tennessee, and a big state park on the interstate, west of Nashville, though their names escape me, that have good deer hunting. All of these places, though, are apply and draw special permit hunts, which are by lottery I think. Even then, they are crowded.
Good news is, there are tons of deer in Tennessee, and it is generally easy to find a deer club to join for a fairly reasonable price. Some of them have as much as a 1,000 acres.
Hardeman County, which is southwest of Nashville, is typically the no. 1 deer county in the State. It is overrun with deer and wild turkey, and there are lots of clubs. It is a combination of swampy land and very dense, hilly hardwood forests. The town of Bolivar is in the center of it all. (Pronounced Ball- ah-ver, with the accent on Ball.)
There was an Article in the Memphis paper about 10 years ago, about a man who deer hunted with every possible special permit and on every legal day of hunting, with rifle, muzzleloader and bow. He legally killed 26 deer in one season.
Deer do not generally run big in Western and Central Tennessee. 120 to 160 pounds is about the average, even for a large buck. There are larger deer in the mountains of East Tennessee, but I have never hunted there.
If you are a squirrel hunter, then you are in luck. There are tons of squirrel everywhere in Tennessee, and very few people seem to hunt them anymore. You can hunt them on the public lands, which have lots of hardwoods, without much problem.
Also, in the southwestern portion of Tennessee, there are now tons of turkey. Twenty years ago, Tennessee started a very aggressive release and restocking program in many areas, using birds trapped on the famous Ames Plantation in Hardeman county, and the comeback has been amazing. Look to the two large state parks I mentioned.
I owned a 52 acre wooded place in Fayette County for 15 years. When I first moved there, there were zero turkey. Five years later, I started seeing a few. By the time I left it, there were wild turkey walking through my back yard. And of course, there were always plenty of deer
Quail are few and far between. Chemical spraying, and planting to the edge of the pavement, have ruined them. Rabbit hunting is still possible, but you need a pretty big farm to hunt, and at least two dogs. There are plenty of beagle hunt clubs the last time I checked.
The Nashville area is highly populated, and its suburbs go way way out. So, you have to drive about 60 miles outside of town to get to the good hardwood hunting. (Unless you own a place with 30 acres of hardwoods or so, in which case there will definitely be deer there.)
The ability to walk up to a farm and ask for permission to hunt is nil. Everyone who has a place either hunts it himself, or has tons of relatives who want to hunt it.
Tennessee is a deer-huntin, rifle tottin state. Never met a person who hunted deer with a shotgun.
It is extremely gun friendly. As I have said before, the difference between a Tennessee liberal and Tennessee conservative, is that the liberal got his carry permit first, before buying his handgun. The conservative already had his piece.
Hope this helps you out.
Mannyrock