This is not from experience, but I've been looking at doing some biking/camping in NC, so here's some food for thought:
Out of Durham is a bike/ped trail, the American Tobacco Trail, that goes almost due south almost to Jordan Lake where there is a campground. It is not 100% paved, but I've been the length of it on my touring bike with no issues.
From Jordan Lake, I think it's a day's trip to the Uwharrie National Forest. Never been there, but it's on my todo list.
Looking along the line from Uwharrie to Altanta, I see another national Forest, Sumter, that looks promising, but it'd be a very ambitious day. I see a small state park, Landsford Canal State Park, about 80 miles from Uwharrie and 50 miles from Sumter. It might make a good stepping stone. I don't know anything about the SC stuff. I've only looked into the NC camping options. Beyond Sumter it looks like there might be a number of park options for camping. I mapped it out just picking nicely-spaced out state parks and national forests, and it made for long days, but it could probably be stretched out more (http://maps.google.com/maps?f=d&sour...9&z=7&lci=bike).
Also this is a generic Google route. I haven't biked beyond Jordan Lake yet, so I can't vouch for the quality of those roads.

I agree with Rapport that Asheville a nice area. However it looks to me like it's off your route and it's also in the mountains, so it depends on how leisurely of a trip you want to take.