Im originally from Cleveland, TN. About an hour south of Knoxville.
There are plenty of places to camp, so dont worry about that. As far as trout fishing, I only know of a couple places i would always go up on the Hiawasee river. The trout were mostly stocked weekly during the spring and summer, but it was still fun. I believe the Smoky's offer a few trout streams, but you'll have to look them up.
Deer hunting is not bad. There is a lot of public hunting in TN, just google it and you will find all kinds of stuff. Im sure you can get on a lease if you want too. Might be a better option. The deer are getting bigger all over the state the last few years, not like the mid-west, but there are plentyof them. A ton of turkeys also in recent years according to my friends that still live there.
You won't be too far from Gatlinburg, and the Great Smokey Mountains National Park. Always nice to go to, just try and avoid the peak tourist season, gets a little crowded.
Oh, and the black bear population has exploded in the park in recent years.
So, you should have enough to keep you busy. Let me know if you have any more questions,