It's my daughter's 19th birthday, and we're spending two days in New York, seeing a show and shopping in the village. I'd want to take her to a few great dinners. She has sophisticated tastes and ideally, I'd like one special dinner the first night for her birthday, and the second night, after the show, a light meal at a fun, hip and happening place (we'll be staying at the Hotel W in Union Square). I actually have reservations at Babbos for the second night, but now am having doubts that it might be too uptight. And between Gotham and Gramercy, which one has the better atmosphere, ambiance and of course menu? Are there any other places that might be better?