Ocracoke airport (W95), open from dawn to dusk, is about 2 blocks from the beach on the Cape Hatteras National Seashore.
It takes about 1 hour to get there in the XL 2 or about 5 hours driving (if you time the ferry right).
If you want to get away from it all, this is the place on the beach.
If you would like a good meal, the town of Ocracoke is only a short 1/2 mile walk away.
The airport gets crowded on holiday weekends, get there early or you won't have a place to park.