For dinner, I can recommend Cafe Moxie in Vineyard Haven but call ahead to make sure you can get vegan, not vegetarian. (They always have a main course that is based on vegetables.) I can also recommend Lattanzi's in Edgartown. Delicious menu that includes pasta. Again, I'd call ahead.
I'd also try giving a call to the following places who I am certain would work with you as they are quite personal and innovative: The Outermost Inn, Atria, Detente, Mediterranean, Sweet Life or Balance. The chefs at these places should be happy to create something for the vegans in the party,. There are not any restaurants that are really focused on vegetarian or vegan dinners. If you go for lunch, try the Scottish Bakehouse.