go to the top of the Empire State Building, including the IMAX attraction they have there.
go see a musical a Broadway. If money is not an option, the Jersey Boys is a must see.
spend a day walking the Financial District. Ground Zero, the river walk on the Hudson, Battery Park, Wall St to South St Seaport. From South St, take the 1 hour Ferry tour up the East & Hudson rivers which passes right in front the Statute of Liberty. Do not spend most of one day just going to see the Statute. Can also walk over the Brooklyn Bridge, with great ice cream and pizza awaiting on the other side (scenic views).