Morehead City is nice, as is Beaufort, NC. So is the NC OBX, I love that whole area.
But you're right, there's not much oystering there, because there isn't much tide, not like we have here in SC. Most oystering there is sub-tidal, and done with tongs.
Anyhow, if you're ever up this way anytime from October to May and want good local oysters, check out Nance's restaurant. Out of all the restaurants in Murrells Inlet, Nance's probably the best view. You can actually see the harvesters working on the flats behind the restaurant, and watch them bring in their day's catch to the hill. Been that way since 1966. I remember eating oysters there when I was little, long before I moved to the area and actually started as a commercial harvester.
Or, if you want to actually get your hands dirty, let me know, I can take you out to one of our commercial shellfish leases and we can grab a handful of nice singles,bring them back to the hill, and wash 'em up in my redneck oyster washer! We'll even swing by the creek where I took Larry the Cable Guy and got him bogged up to his chest in pluff mud, we've got a sign marking it as the official film site of that show. 8)