Drive a little north (not that far) to Calabash, NC. I can't remember the name of the place, but across from the Christmas store is a little seafood place. It has a sign that says something about it being the original...
It really isn't hard to find. We only had the shrimp there, but it was fantastic! I don't know if they are open on Thanksgiving--we were there in the summer a few years ago. We went there for the dolphin tour, which was fantastic, albeit very wet, and had lunch at this place.