Not much happening running wise in either of those locations. You could go to a place like Virginia Beach/Hampton Roads but honestly the running there kind of sucks. Virginia Beach has the boardwalk to run on (keep it on the 'crete!) And a state park but that is about it. Even the State Park isnt that great as it's a lot of out and backs and multiple times on same trails to get any type of mileage.
You could do a combination of some stuff up in Williamsburg/Newport News/Yorktown and Virginia Beach and get some okay running in and a little bit of hill work up in Williamsburg area. Better trails up there, as well.
Other than that, almost all of "Southern Virginia" and "Northern NC" are pretty damn rural. Don't expect much of a bigger area or good running.
You could do Raleigh area. Nice bike path and trail system...head to Umstead State Park and get some good mileage in..plenty of trails and good elevation in the park. Nice area between there, Durham, etc