Q-Man and Captain
I assume you're not joking, but just have not looked at any charts
Corolla, NC on the Outer Banks
is located about 34 miles south of Norfolk, VA along a nearly unbroken Atlantic Coast, with no usable inlets nearby. Furthermore, on the inland side is Currituck Sound which is very shallow. You couldn't get a Morgan
34 anywhere close to Corolla.
Nearest deepwater port is Coinjack, NC which is on the Intracoastal Waterway about 5 miles west of Corolla across Currituck Sound.
So, to answer your question, a good route
from NJ might be to sail down the coast to Atlantic City, up Delaware Bay to the C&D Canal, down the Chesapeake Bay
to Norfolk, enter the ICW
at Norfolk and head
south through Currituck Sound to near Coinjack. There ain't much there, though, and you can't drive from there to Corolla.
All-in-all, I think I'd choose another destination