I'm not familiar with the territory, but there are some places to start according to
FIRST's list of North Carolina teams.
Of them, your best starting points seem to be 435, 587 (which is actually sponsored by Duke, according to their team name), and 900. I don't know about the rest (though I do know that 1225 is on the other end of the state, as that's where my mother's family is from).