Much of the following is common sense: great sites, galleries and culture venues almost at every street corner, abundant wonderful restaurants and convenient transportation. You can never exhaust the city but neither can other people, so the streets are filled with travelers every day. And naturally, expect to spend twice of thrice the money on food, accommodation, etc. as you would elsewhere.
Insider Tip:The Staten Island Ferry is a free ferry trip that allows you to see the Statue of Liberty from a distance--the perfect distance for pictures. If you want to visit the statue itself (many find it unnecessary as you would be too close to have the full view of the statue) you need to make reservations way ahead of time, especially if you want to climb all the way to the crown.