I can't speak for the food, but we had drinks at the bar recently, and whew was the service awful. Condescending bartender who was really unwilling to help a group of 4. She basically laughed in my friends face when he asked what her specialty drink was. Yuck.
Romantic? Not at all. Birthday? It depends what you're looking for. If you're looking to go to an iconic New York restaurant and aren't that concerned about having amazing food, then it could be fun for a party.