Yes, a UNC-CH carries weight in NYC and DC. I cannot comment for the west coast since I am not from that area. However, UNC-CH is nationally known.
Like the west coast, the east coast is not homogenous. I am originally from the NE and many in the NE will dream of going to the Ivies and put the Ivies on a pedestal. Many will also look at UNC-CH and UVA both for their prestige, lower cost and more importantly for the quality of education. Many will look down at the their our state schools even though some of them are excellent. I am now living in NC and it seems that the dream of many kids is to go to UNC-CH. We take great pride in our state schools. In addition, there will be many kids at UNC-CH that got accepted at the Ivies or had Ivy type stats and choose UNC-CH. Many due to financial reasons.