As other posters have said take some training. Get comfortable with performing self and assisted rescues. Always try to paddle with at least one other paddler.
Depending on where you live, there are several rivers along the NC/VA border. A few of them are the: Dan River; Roanoke River; Meherrin River; Blackwater River; Nottoway River; John Kerr Lake; Cashie River; Tar River; Fishing Creek and etc..
Naturally you would want to avoid any river while it is in a flood stage. This website
http://www.srh.noaa.gov/alr/ahps/ahps_RVFNC.shtml gives you some indication of what is considered flood stage for the above rivers.
You would have to take a closer look at each of the rivers to find water conditions to your liking.
Don’t forget the Inter Coastal Waterway, Dismal Swamp, local bays and estuaries. There can be a lot of nice paddling in these.
Some time ago I did some boating in, and around, Albemarle Sound and its rivers. It can be very interesting place to paddle. This web site lists some Carolina Water Trails.
http://www.watertrailslocator.com/
north_carolina_water_trails.htm
A couple of books that might be of use. I’ve not read the first two myself. I’ve read one of Ed’s other books on paddling Maryland. The book was a bit old. The waterway had changed from when he had paddled the waterway. His general descriptions of the water and directions for put ins and take outs were still relevant.
The Wild River Guide to Dismal Swamp Water Trails is a journey to the wilderness heart of over 20 historic waterways in northeastern North Carolina and southeastern Virginia.
Wild River Guide to the North Landing River and its tributaries is the guidebook for the southern Virginia Beach and Chesapeake waterways connected to the North Landing River, a state scenic river for Virginia.
Exploring Flatwater: Northeastern North Carolina, The Outer Banks, and Eastern Virginia by Ed White
Daniel