I am not vegan, but I have some serious allergies that are pretty easily accommodated by a lot of vegan restaurants. So, assuming that you're in New York, some of my favorite spots:
Candle Cafe (Candle 79's more casual and more reasonably-priced outpost. Originally on the Upper East Side, but they just opened and Upper West Side location. Delicious and you can often get two meals out of an entree. One of my favorite restaurants, period)
Josie's (Creative, tasty, healthy vegetarian options -- they are super accommodating to dietary restrictions of any kind)
(Cafe) Blossom (I like the one on the Upper West Side... 83rd and Columbus, I think? but they have a few other locations that I haven't been to, though I do know the menus vary a bit. They also just opened up a fast food-type place somewhere on the West Side)
Peacefoods Cafe
(Of course places that are vegan won't have dairy or eggs, but the tradeoff is that a lot of their food is more creative the run-of-the-mill salads and whatnot you might be stuck eating in some other places. And if you are concerned about protein, because the ingredients on a vegan diet are even more limited, they're sympathetic to those issues, too.)
Falafel (almost anywhere) is also one of my favorite go-to things when I'm out.
And if you are ever in Chicago, do yourself a favor and check out the Chicago Diner. All vegetarian, mostly vegan, but classic diner and comfort food.
A work of art is an invitation to love.