Nags Head (near Kitty Hawk in the NC outer banks) has some neat lighthouses
Lighthouse Tour and Directions
Chimney Rock
Chimney Rock Park | North Carolina hiking trails with incredible mountain views is also near Asheville, NC
Lake Lure has a quaint Inn
Discover Lake Lure, North Carolina - The 1927 Lake Lure Inn and Spa near Chimney Rock.
Sorry this isn't very organized. I'm writing the places as they pop back into my brain from my ancient memories.