Are you wanting to backpack or just park and camp? If its a park and camp, there are several state parks near Raleigh and you wouldnt have to drive 4 hours. Plenty of swimming holes and modern amenities (drinking water, toilets, etc). If you want the mountains, look into National Forest campgrounds. You can park at your site and day hike from there. If your wanting to backpack, well thats a while nother can of worms. It just depends on what type of experience your looking for.
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Climb the Mountains and get their good tidings...
-John Muir