Second on Ocracoke, but it'll be some time...maybe down the outer banks, see the lighthouse, then 1/2 hr. ferry to Ocracoke, drive across it, then 2 hrs on the ferry back to mainland (you'll be at the bottom of the Outer Banks, then). Eat at Eduardo's Tacos (we like the shrimp tacos). If you're interested and can't do Outer Banks, Raleigh's North Carolina Museum of Art is a very good art museum.
If you do Outer Banks and need a place to stay, as soon as you get off the Ferry back on mainland at Cedar Island, there's a small hotel/campground recently renovated that has horseback riding on the beach, kind of cool.