First off, NY is not just Manhattan Island! It is also a State even though some dont know that!
What DeltaAlum said! Ride a Bus to see what is around!
I did this in London, and The Tram in Viennia.
Get the lay of the land.
Go to Statue of Liberty, Ellis Island, MSG, Radio City Music Hall, Top of the Empire State Building, Yankee Stadum.
There is much to see and never enough time!
Cabs, look out!
Will give you a quick tour if you dont know where you are going! $$$$$$$!