I am posting this as a follow-up for anyone who may find this thread through a search.
The trip was BEAUTIFUL! We enjoyed seeing the area, taking a boat tour, shopping, and visiting with local artists. Very relaxing and wonderful.
We were able to eat and did not starve.
Beaufort is tough. We did find subs and pizza at
No Name. The only place in historic Beaufort that we found to eat was the salad bar at
Ribeye's. (Thanks so much for the recommendations above!) I read every menu that I could find online, and I did not see any options. So I contacted all of the restaurants with an online presence and asked if their chefs would make something vegan. None responded.
We also ate in Morehead City, which is very close. There are several
El Zarape locations, and they have a nice vegetarian menu. There is also a
Panera Bread.
We stayed at a place with a fridge, so we picked up breakfast and snack items. We packed our own lunch to take out to Shackleford.
It's not a vegan paradise, but it's certainly worth the trip.