I did 7 days in NYC the christmas before last. 4 days is plenty.
I was trying to do it on a budget so stayed at a place called the Ravel hotel in queens, just over the Queensborough bridge. Average hotel but only £70 a night, which was about half the price of anything in Manhattan. However the view from the rooftop breakfast bar was worth the price alone...! http://www.ravelhotel.com/
Things to do...
Helicopter Tour
Boat trip to Liberty Island
Central Park (just to hang out on Literary walk is awesome!)
Tea at the Plaza Hotel
Go and find the Friends apartment
...
...but the best thing i did was go on The Sopranos tour! If you're a fan you have to go on it. Got to go to loads of locations, and i got to meet Vito from the show, and have a few shots of Tequila in the Bada Bing!