The Butcher's Daughter is an awesome eatery in Nolita. It is completely vegetarian and dairy free. It's also a juice bar, and everything I've tasted has been delightful.
They do serve eggs, so if you're vegan, make sure to let them know.
The Ploughman's Lunch is an assortment of cashew cheeses, pâté and veggie sausage, served with bread and fresh cucumbers.
The BLT is made with heirloom tomatoes, adzuki bacon, bibb lettuce and basil mayo (with a side of watermelon cubes - how cute is that?).
The Merguez Sandwich is filled with spicy veggie sausage, fig mostrada, seasoned vegan mayo and greens. This one is my favorite. It's spicy and sweet and really filling.