I'm live in NYC,I would say:
*$12 Ice skating in Bryant Park or Ice Skating in Rockafeller Center.
*Walk down 5th ave and view the holiday windows in the department stores
*FAO Schartz toy store!Its a treat!
*If you have some more money to shell out,visit the top of the empire state building
*Times square is a tourists spot with stores such as Toys R Us that has a ferris wheel inside the store! The M&M store is fun too!
*A fun shopping area is the Soho area,also Noho
*Central Park of course,tourists seem to love.You can get a ride in a horse drawn carraige,poor horses :(
*You can visit the world trade center site down in the financial district
*Broadway shows at discounted prices
*Also off broadway shows like something at the Public Theatre over on Astor Place.
*MOMA (Museum of Modern Art)
*The Met,Whitney Museum,The frick,Guggenheim etc
And now...for Brooklyn!
Brooklyn is now one of the hottest boroughs!
*Explore Williamsburg! A lot of small creative shops off of bedford avenue.
*Tons of fun bars!
*Fun coffee shops
*Art galleries etc
*All of these things extends into Bushwick
There are TONS of things to do in NY -- catch a show, go on a tour bus to take in the holiday sights and sounds, take a walk through the park and go ice skating, get to the top of the empire state building, have dinner at the time square Marriot...
Walk across the Brooklyn Bridge, pub-crawl along the seaport, etc. etc. etc.
The sky's the limit. Don't be afraid to take a bite out of the big apple, haha.
There are many websites with great ideas and info about everything. The other answers mention some great stuff. I will be in NYC for 2 weeks. If you are gonna be there on Sunday the 13th, join the No Pants Subway Ride. Find info on ImprovEverywhere website. Enjoy your visit.
Take the F train to Coney Island...
go see the ocean
Watch the New York City's NY Knicks.
Have some adventure, it's important to not include lunch dates.