Without giving us an idea of what kind of food you and your seven year old like, it's a little hard to advise you. As you will see on Happycow, there is probably a greater choice of vegetarian and vegan restaurants in New York than in any other city in the world. Literally all styles and types of cuisine. Give us some more info and I'd be happy to give some suggestions
Paul (Co-organizer, New York City Vegetarian Meetup Group)
My daughter is a typical 7 year old, "junk food" (burger, fries, shakes, dessert)...we try to keep it "healthy" junk food . She also loves Asian food....rice and vegetables, tofu spring rolls. I'm also looking for something in the theater district (due to a 2:00 matinee we will be attending). My partner and I enjoy all cuisines and are enthusiastic about trying different foods. Basically, I'm searching for kid friendly restaurants. Thank you.