Fly into Raleigh-Durham Airport and rent a car to drive to Outer Banks, NC. The drive is about 4 hours. Some locations on the Outer Banks require a car that has 4 wheel drive (in Corolla). If you want to do this in 2 days, that is a good option. There's tons of good food places and places to stay in Raleigh, Durham or Chapel Hill.

Fly into Norfolk International Airport (ORF) and rent a car and drive to the Outer Banks. The drive is about 2 hours. Some locations on the Outer Banks require a car that has 4 wheel drive (in Corolla). I'm not as familiar with this area and can only recommend googling if you want to stay in the area.