If you can still get a reservation at Tavern on the Green, do try it and enjoy! It's a landmark restaurant that overlooks Central Park, giving you a romantic Manhattan experience. On a whim, we walked-in one autumn day and had one of our best dates ever. The ambience, the food, the staff, the attentive maître d', the music... hmmmm...*starry eyes*. This was years ago, when we were still new to the city and we had a mental list of places to check out from the Romantic N.Y. book. :P The crystal room is what they say it is... fabulous! You've got to see it to appreciate it.
Another good choice would be One If By Land, Two If By Sea. I went there during summer restaurant week. Although I picked the place, I didn't know that it's been voted as the most romantic restaurant in the city. I went with a girl friend, and well... too late to realize that we could have brought the guys. We were also busy gabbing away. :)
What I would really love to try is River Cafe. Big Al, are you reading this?