Places to visit - Jockey's Ridge State Park (milepost 12) has the largest sand dunes on the East Coast, plus a great visitors center.
You can also climb both the Bodie Island and world famous Cape Hatteras Lighthouses. Both of those are on Hatteras Island. Bodie is only about 20-30 minutes south of KDH, Cape Hatteras is about an hour, but it's a gorgeous drive down NC 12.
If you're looking for a day trip, drive 90 minutes to the southern end of Hatteras Island and drive on the free ferry to Ocracoke Island. Quaint little village at the end of the island with plenty of shops and restaurants. All local, no chain stuff. Between the drive and the ferry back and forth, you'll want to budget an entire day to do this.