How long will you be there? There is SO much to see, most of it the usual, but some stuff that is not as well known, but worth it. Since you're going to Broadway, you might want to check out the USS Intrepid, the aircraft carrier turned museum. I've never taken a tour of the UN, but I'd personally be interested in other stuff. The most comprehensive art and sculpture would probably be the Met, although MoMA is better for modern stuff, as is the Whitney. There is a Circle Line tour that goes around the entire island, and you get to see really amazing stuff, like mansions on the water, and the skyline of NY from a really fantastic vantage point. But it is 3 hours long. DEFINITELY worth it IMO. There is an excellent (and pricey) restaurant across the river from lower Manhattan in Brooklyn called River View (or something like that. It's right below the Brooklyn Bridge, and offers a stunning view of the city. At the northern tip of Manhattan is something called The Cloisters, also more of a day trip, but very easy to get to on the subway. Thought it's a fabulous excursion, I'd stay away from the Statue of Liberty this time of year - waaaay to cold. But a tour of Financial District (Wall Street) etc., and the fort that defended the early city - Castle Clinton - is very interesting. You can finish up at South Street Seaport - the first successful commercial port reclamation project in the US. A stroll down Fifth Avenue is always nice - and not too pricey if you stick to window shopping. There is a luxury Japanese department store called Takashimaya (?) which has glorious merchandise, but the real gem is on basement level, where they have a tea room with dozens of incredible teas in a true zen oasis. There is just way too much to see and do, so just go with the flow. It flows fast...
You can look all these things up online to get more info.
The Brooklyn side just under the bridge has great city views... Not brilliant in the winter but great views.
Top of the Rock is great - late afternoon before dark so you get the transition... I had no issues with a little table top tripod and on the top deck there is a thick brick wall and you are over all the glass walls so clean air, so nice place to setup. I was up there a week back actually and with the cold air the photg is great - IF you can stand the cold :-) Can get a tad windy up there also :-)
The plaza opposite radio city has some great looking large xmas balls and with the radio city in the background makes a great shot.