92AF, Welcome to OCDO. Keep asking questions. There is a GREAT group of people on here that can help you navigate the confusing rules, laws, and statutes of NC Open Carry.
Here is a link to the Municipal Code for Mooreville, NC:
http://library1.municode.com/default-test/home.htm?infobase=12288&doc_action=whatsnew
This site has a search function, so just search for "firearms" and you should get all the info you need for your specific town.
As a general rule, OC is legal just in almost EVERY city of NC, with the exception of Cary (no carry on city property, which includes streets and sidewalks) and Chapel Hill (you can't carry guns with "short" barrels).
Some cities have prohibitions on carry in city parks, and if you don't have a CHP, carrying near schools can be problematic, but generally, if it's not a government building (city, state, fed) a restaurant that serves alcohol, or a venue that charges admission (like a movie theater), and it's not posted private property, you are probably OK to carry...
Specific venues, you can ask about. Some of us have been doing this a while, and have got most of the prohibited places (and commercial establishments that are not gun-friendly) figured out. Keep asking questions, and we'll do what we can to steer you in the right direction...
Also, you might consider joining GRNC, they are a NC-specific gun rights organization that is VERY politically active, and are very pro-OC. They fight for our rights when groups like the NRA won't, and supporting them benefits ALL gun owners in NC--CC and OC...
http://www.grnc.org/