http://www.ncwildlife.org/
The striped bass season on the Roanoke River is just ending. It can be a bit of a zoo sometimes, and if you make someone really angry, maybe they shoot you, but it is a world class fishery. For flyfishing, unless you are in shallower water, you need to be able to get deep quickly.
Fish in the 30 lb range are not unusual, and they can get bigger than that. I think that the shad run is just a little bit earlier, and there may be some overlap.
I think that this link will get you to the general wildlife department site, where you can choose the site of interest.
Note that North carolina offers some thousands of miles of trout streams at the other end of the state, plus a wide variety of saltwater and brackish water fisheries. These range from site fishing for redfish in the sounds, to blue water fishing in the Gulf Stream (marlin, tuna, mahi mahi, etc.).
Note that North Carolina requires no written test for a fishing license, even for Germans.