1. Hit China Town for some fun and inexpensive souvenirs (you can even grab fireworks).
2. Hit Battery Park. Stick a quarter in those binocular things so you can get a great view of the Statue of Liberty.
3. World Trade Center is a must - go see the view from the top.
4. Central Park, obviously. But not at night.
5. Do you have kids? New York really has some of the finest toy stores in the world. They're fun if you're an adult too. Definitely worth checking out.
6. Try to see the symphony at Carnegie Hall. Obviously the list of musicians who have performed there is unmatched. Ella Fitzgerald, Count Basie, Frank Sinatra, Luciano Pavarotti. And actually it's not that hard to sneak in for free if you're pinched for money.
7. If at all possible, stay a night at the Plaza. It's absolutely New York's most exciting hotel experience.