Relevent law can be referenced here: For concealed:
www.handgunlaw.us, and for open carry:
www.opencarry.org The NC specific link is
www.opencarry.org/nc.html
Both have links to the actually state law, as well as a summery. Both are good reliable sources and are update as soon as the local state law changes. Be aware that neither covers local law, just state law.
It is best to go to the state laws and read them for yourself. The summeries are ment to be guides to help you understand what is written. some legislatures actually have links to court cases too, which is very helpful.
It may be especially worth your time to check out OCDO (open carry) if you do not intend to obtain a concealed permit. They have a forum for each individual state. It looks to me like Durham county has some funny stuff, but the rest of the state looks fine for OC without a permit.
You need to read the law though