For Prime Rib and Steak and a hip New York attitude, I love Dylan Prime. Say your are from LCT and ask for Mike Waterhouse you should get charming service).
Nobu is my favorite worldwide restaurant..in NY, LA, London, Paris....very hard to get reservations. But if you arrive at 5:45 at Nobu Next Door,you should get in. Even the President of Takeda couldn't get into Nobu this week!! It is not a NY institution, but it is a wonderful place.
I do not like the others Doug mentioned as much as the two above. Tribeca is less about the food and more about where to be seen and Chanterelle is about the food, but is a little to uptight for me.