I was there for my 40th in November and there are 2 places that spring to mind especially.
Firstly is BuddaKan, its a kind of modern swanky oriental almost fusion place, the food was very good and it wasnt that expensive for what we had
http://www.buddakannyc.com/The second place is 'the counter', a burger chain with a restaurant just off broadway, and its awesome, have a look at the menu and you will see the way to order and what you get
http://www.thecounterburger.com/menu/ the apple pie milkshake is pretty good too.
I never went personally, this time, but the River Cafe under the Brooklyn Bridge is meant to be good, $100 fixed menu option gets highly recommended.
Ian