I'm a mountain guy, not a beach guy
UPDATE (29 July 2010): Added some links and a map, but content is as I wrote it eight years ago.
I just got back from 2 weeks on the Outer Banks of North Carolina. Don't get me wrong, I enjoyed myself. I'm just not into sitting on the beach and soaking up the rays. I enjoy a good pounding surf, but I'm not much into swimming for recreation. I'd rather be hiking. And there's not much of that to do at most beaches.
There are trails on the Outer Banks and nearby parks. The Alligator River National Wildlife Refuge has some, but the bugs are evidently immune to repellant. It's really hard to enjoy a walk when you're flailing away with your arms. It makes it difficult to view the scenery. And there were other trails on Pea Island, Buxton Woods, and Jockey's Ridge, but none longer than a couple of miles.
One pleasant location is the Nags Head Woods Ecological Preserve run by the Nature conservancy. They have about 4 trails totaling just under 10 miles, but I found them to be pleasant, with a surprising amount of elevation change. I also walked away with a good ghost story which I can tell you over a beer sometime.
View Nags Head in a larger map