The delay in answering that question is that I drew a blank. I even reached out to a few friends and the response that came back was equally dumb-founded. I did get two possibilities:
1. Sunset Grille in Duck, but that is ... Soundside.
2. Another thought was the Sanderling Inn. I just don't know if they have ocean front tables.
The reason why this is a hard one is because most property that is oceanfront are rental houses. Rent an oceanfront house and you can have seven romantic sunrises.
Another possibility is the Ramada in Kill Devil Hills. It is oceanfront, but whether the restaurant is oceanfront, I am not sure, but you could give them a call at 252-441-2151.
But I have one more idea. If you truly want a private, romantic place for breakfast that is oceanfront, maybe consider packing your breakfast and head out to the Cape Hatteras National Seashore just south of Nags Head and pick out a spot.
So, basically, since I've been little to no help, I will open this up to others to respond to. Any help ... please?