Be aware, some areas of established public "Game Lands" are open to hunting but closed to camping.
I live here so I would suggest Pisgah National Forest in the western end of the state. Somewhere around the Mills River area. There are a lot of deer (I assume that's what you want to hunt) in that general geographic region, a few hunt clubs, private land etc. The Pisgah NF borders a lot of prime private land. There are deer throughout this area as well as squirrels, bears, turkeys, grouse etc.
You can backpack and camp most anywhere. Car camping along the roads require you stay in an established site. Backpacking in will get you some privacy, and go in a couple miles or more will get you away from most hunters.
Be aware, because of our relatively mild climate, day hikers and mountain bikers are active year round.
Get a copy of Nat Geo "Trails Illustrated" trail map, available at local outdoor places, REI, etc. National Geographic Maps | Pisgah Ranger Districit
It will show every established trail in Pisgah NF. It also shows trails that are closed to horses and/or Mtn biking which is important if you want to hunt or don't want people riding past or through your camp.
Around Mills River, some of Pisgah NF is a bear sanctuary and closed to bear hunting. And speaking of bears, wherever you go, hang a bear bag. Several areas have been closed this Fall because of inexperienced campers keeping their food in their tents.(?) At least 3 incidences the bear tried to gain access while the campers were inside!
That's about the best I can do for you. Lots of NF land available for exploration. Get away from the roads and you'll find privacy. A lot of our mountain land is impenetrable tangles of laurel and rhododendron so you'll definately need a trail map. A lot of areas are simply not navigable trying cross-country. Fortunately there is an extensive trail system.
If you want to take a day sight-seeing hike for photos, I would suggest John Rock or Looking Glass rock trails...or...A little farther up, get on the Blue Ridge Parkway, head south and hike trails to Black Balsam, Shining Rock, Tennent Mtn, Graveyard Fields. That whole area is great. The views from Black Balsam/Tennent Mtn are open and spectacular. All within a short drive from the Mills River area.
Hope this helps.