North Carolina has a good web page that lays out the major "bike highways" around the state, including a few that might suit your needs. Here's the link. The maps themselves are not great. I recommend a North Carolina Gazeteer, which shows the NC Bike Routes (you have to look closely but they are there -- check the back of the Gazetteer for details).
http://www.ncdot.org/transit/bicycle..._highways.html
It is nice and flat along the coast, including the inland port towns, but beware of the wind. It's often said out there that "the winds are the hills." I did a mini-tour of the Outer Banks last spring and was surprised by a change in weather that had us cold and in the teeth of the wind for several days. Just be prepared and bring layers, we we did, and you'll get through alright. In fact, thinking about that, you'd be better served with the "Ports of Call" route compared to the Outer Banks this time of year. Small towns like Elizabeth City and Edenton can be very charming in the off season.
Feel free to send me a private message if you have more questions.
Ken
Durham, NC