As above a walk around central park is a must, plus the lower east side for diners as well as some great places in Greenwich Village, especially the best pizza ever (including Italy in my opinion) at Joe’s Pizza on 6th and Bleecker.
Then head down to battery park and catch a ferry tour over to Ellis Island (no trip to NY is complete without out it in my view)
Central Station is a must with another great food spot, head on down to The Oyster Bar in the basement, miss the high price stuff and head to the booth on the side of the restaurant which does take away at low prices.
The best bet by far though is to book a Big Apple Greeter ( big apple greeter[/url] )
It does not charge and is real New Yorkers giving their time up to show you around. You have to book but its the best 3 hours you can have.
We got a retired Columbia University professor of Architecture, who gave us an amazing walking tour as well as free passes for the Metro which got us over to Brooklyn so we got the best view of NYC and a great walk back over the Brooklyn Bridge.
Give it a try cos its free !!