Apart from the numerous famous tourist attractions in one of the most exciting cities in the world:
Staten Island Ferry
Wonderful views of Lower Manhattan, Statue of Liberty and Ellis Island.
It used to be the best value for money trip in New York @ 50c each way, but I think it might even be free now.
Bar at the Rainbow Grill (Rockefeller Center)
Perfect for a relaxing nightcap after a busy day's sightseeing - stunning views of New York at night from the 65th floor bar.
There's also an observation deck.
Marriott Marquis Hotel, Times Square
47 floors up - and the only revolving bar/restaurant in Manhattan, I think. (The Rainbow Grill is 18 floors higher so IMHO the view is even more stunning.)
River Cafe, Brooklyn
Water Street, immediately next to the bridge on the Brooklyn side. Spectacular view of Manhattan across the East River, day or night. Good place for a drink/snack at lunchtime. Dinner isn't cheap but, if you get a window table, IMHO worth it for the view.
Helicopter tour
Simply amazing.
Carnegie Deli
Seventh Avenue, at 55th Street. Famous deli, reputedly the best in America (although IMHO not as good as Nate'n Al in LA.) Good food and a New York experience. Always a long line - no reservations - but worth the wait.
Tips:
#1 Miss breakfast and go for an early brunch before the lunch rush starts.
#2 The portions are absolutely enormous - a 'sandwich' is a full meal - don't over-order.
Christmas decorations at Rockefeller Plaza
Always a fabulous display. The enormous Christmas tree will be lit by now. Lunch at the outdoor cafe watching skaters on the ice-rink is an enjoyable experience even if, like me, you can't skate.
Just walking the streets of Manhattan
I'll never forget the first time I walked amongst the skyscrapers - almost 30 years ago - and I still find it a thrill every time.
Airport to Manhattan
The helicopter shuttle has started again. No idea how much it costs - but what a way to arrive! 
Otherwise, I recommend taking a taxi or bus from the airport. The view of Manhattan as you approach is very impressive. The subway is quicker, but you'll miss the view.
New York taxis
Know exactly where you want to go before you get in and keep the instruction as simple as possible - preferably just the avenue and cross street. The Manhattan grid layout makes finding your way around easy but, for some reason, many NY taxi drivers don't seem to find it so.
Have a wonderful time. 
FL
Last edited by Flying Lawyer; 8th Dec 2007 at 04:48.