I dunno if you wish to travel a ways but up in Boone NC or around their there are alot of places to back pack and camp. Particularly around the blue ridge parkway area. My favorite places to back pack.
If you're up to traveling out to the Appalachians, then the Appalachian Trail around Hot Springs is an amazing place to go for a trip. There are some great places around Asheville too such as the Mills River area.
Linville is awesome, as is anywhere in and around Boone and Blowing Rock. You can pull off of the BRP at pretty much any cutout and find a trail or two to just explore and find some really great views.
With a bunch of guys. Some how we took the wrong way and went the really long way to the camp site at the back side of the park. Est about 12 miles and hiking into the night. Man was I sore.
I got on that same trail one time with my wife and daughter we were all
literally crying wondering when it would end we were so tired. Saw 2 rattlesnakes.