I was emailed a document from the public information officer of the North Carolina State PD. The document does not specifically address openly carrying in a restaraunt. It does say concealed firearms are prohibited in restaraunts. So, my assumption is that OC in NC restaraunts serving alcohol is permitted.
See the PDF below:
The PDF does further clarify that, by common law, "Going armed to the terror of the people" with a dangerous and unusual weapon is unlawful and that any firearm fits within this provision. This link
appears to be a/the case where this was established.
I don't live in NC, but have been brushing up on gun laws in NC because I visit 2 - 3 times a year (and am there now, as a matter of fact).
IANAL, so don't take this as gospel or counsel. I encourage you to research your particular scenario and make your own judgement.