I'm confused.
If you are going to NC, you need to go SOUTH.
Anyway, you need to get to I95, the only reason to go West is to get to I95, and that simply means getting over the bridges or tunnels.
Here's a thread that talks all about going south (to Florida):
Driving from NYC to Miami, Florida. Any suggestions?
Its not mentioned, but you can go over the Verrazano Bridge into Staten Island, the SI expwy to either of the two bridges into NJ, then catch I95 that way. This route requires a very early leave, as rush hour traffic to and thru Staten Island is totally brutal. 5am at the latest. Earlier if you want to beat the DC/VA rush too.