Here's another welcome.
I retired here to Cleveland, a bit northeast of you Hamilton Co. folks. Been here since 2000. I don't know much about the hunting lands west of the Tennessee River, up on the Cumberland Plateau. There are several state parks there that I know you can hunt. I have tried it over there, but I had a couple of confrontations with locals, so I tend to stay away from the Cumberland Plateau now.
However, I know the Cherokee National Forest pretty well from the Tellico Plains district south to the Georgia state line. I used to volunteer on a trail maintenance crew and so over the years I think I have been on every trail south of the Smokies down to Georgia.
It is all very rugged mountain terrain with steep sided ridges and deep, rhododendron choked ravines. In fact some of the larger rhododendron and mountain laurel thickets are locally knows as "hells". "Jeffery Hell" in the Tellico forest district is one of the worst to get tangled up and lost in.
Hunting is tough!!! Yes, I put extra emphasis on tough. Packing out a big game animal may be even harder.
First; Bear. Everything in the Cherokee south of the Ocoee River to the Georgia line is a bear reserve. NO bear hunting allowed there. Other game is okay. There is another bear reserve up in the Tellico district.
If you don't have a pack of hounds to follow your chances of getting a bear are mighty slim. Baiting is probably the most effective way to get a bear, but of course baiting is illegal in Tennessee. However, an alternative might be to find a well used game trail that passes through a funnel area, such as a gap in a ridge, then sit there and wait for a bear fleeing the hounds to pass by. I know of one such great spot in the Tellico district, but it is remote, in the Bald River Wilderness Area, and getting a bear out of there would be a major chore.
Deer in the Cherokee are spread mighty thin. Middle and western Tennessee have a much denser population. However there are some nice bucks scattered back in those mountains. Thoroughly scouting before the season is key. Learn to tell the difference between deer tracks and pig tracks. Deer have sharper pointed hooves. Pigs have more rounded hooves.
Wild pigs are everywhere - and nowhere. They can be anywhere. Again, scouting is key. The same advice for hunting bears also applies for the feral pigs.
Turkey. In my opinion turkey numbers in the Cherokee have declined drastically over the past few years. Yet, the big birds are still there, although much more widely scattered than they used to be.
Get a good map. I have a good topographic map that is put out by National Geographic and called "Cherokee National Forest; Tellico and Ocoee Rivers, Tennessee, USA" It is available at the US Forest Service headquarters here in Cleveland and also at either the Tellico or the Ocoee Forest District offices. It is not cheap, though, for a paper map. I don't know the current price. I bought mine years ago for around $10. or $12. Mine is getting pretty worn out - time for a new one. This map not only shows the land contours, but also the forest roads and the hiking trails.
You younger guys probably use modern electronics, such as a GPS. I don't. I'm a dinosaur. I use a compass. Also, I put my modern rifles away over 20 years ago. I hunt all season long, through all the various hunting seasons, with only my traditional muzzleloaders. Percussion and flintlock. Traditional. I wouldn't touch one of those abominable in-line things if you paid me. But, to each, their own. I took a nice 6 point last season with my .50 longrifle.
Get a good map and start exploring.