I was in this same position 3 years ago. Choosing UNC (I'm in-state btw) over NYU was the best decision of my life. Even if you're out of state, UNC is a way better deal than NYU. We have a great classics department, too. They are totally different college experiences though and depends on your preferences. UNC is the paradigm of a "college experience" & Chapel Hill is the prefect college town whereas NYU doesn't really even have a campus.
Also, I know plenty of people here at UNC who intern over summers in NYC so although there are opportunities that come with living in the city, it doesn't give you that much of an edge over equally qualified students in other colleges.