OK, after searching MuniCode, I found this in the Town Ordinances of Nags Head:
Sec. 26-2. Firearms and explosives.
(a) Discharge in town restricted. It shall be unlawful for any person to fire or discharge shotguns, rifles, pistols or any other firearm, or discharge any explosive device, by whatever name called, within the corporate limits of the town. The town firing range shall be excluded from this section.
(b) Enforcement. Subsection (a) of this section is enforceable by the town police department.
(c) Exceptions. The provisions of subsection (a) of this section shall not apply to:
(1) Police officers and other duly authorized police and peace officers of the county, state and the United States of America, or the armed forces of the United States of America, while in the performance of their duties as such;
(2) Shooting contests such as turkey shoots, target practice and other contests after a permit has been issued therefor by the chief of police and while the same is under the direct supervision of the chief of police or a designated officer of the law.
(d) Carrying of concealed handgun. The carrying of a concealed handgun as defined in G.S. 14-415.10 et seq. in any building or appurtenant premises owned, leased or occupied by the town for governmental purposes, and in all municipal parks, recreation areas and beach access areas, is prohibited.
(e) Posting of prohibition. The prohibition against carrying a concealed handgun shall be enforceable in any government building and appurtenant premises and on any park described in subsection (d) of this section upon the posting of a notice stating: "The carrying of a concealed handgun on these premises is prohibited and illegal." This notice shall be posted in a conspicuous location near the entrance to any such premises.
(f) Violations. Violation of subsection (d) of this section shall be punishable as provided in G.S. 14-415.21(b).
(Code 1990, § 13-2; Ord. No. 08-01-004, § I, 1-9-2008)
State law references: Authority of town to regulate, etc., discharge of firearms, G.S. 160A-189; regulation of sale, use, etc., of pyrotechnics, G.S. 14-410--14-415.
So it looks like carrying CONCEALED is prohibited on the beach, and any other city recreational or park area where posted. But I don't see any general prohibition on OC...
Anyone want to be a test case?