NYC is my favourite city in the world and try to visit at least once s year. In fact, I'll be there next weekend.
Everyone's suggestions are really good and I'll second the Brooklyn Bridge and Top of the Rock suggestions as both are my favourite things to do. I suggest taking a subway to the Brooklyn side of the Brooklyn Bridge, eating dinner at one of the many good restaurants around there (I suggest Juliana's Pizza is you like pizza) and walking across the Brooklyn Bridge towards Manhattan when it's dark. Might be the highlight of your trip.
i also recommend taking the free Staten Island ferry to see the Statue of Liberty. Although it doesn't go to the island with the statute of Liberty, it goes very close so you can get great pictures. Can't argue with free.
NYC is a perfect walking city so I also just like picking a neighbourhood and exploring it. I like the Free Tours By Foot tour company. They are walking tours with a group of people and a guide. They are free except for a tip for your guide at the end of the tour. $10 or $20 per person is usually what I pay. They have a lot of 2 hour tours, food tours, and even 6 hour all in one tours. The first time I went to NYC I did an all in one 6 hour your after reading about this tour company on trip advisor and it was the best decision I ever made. Saw so much and had so much fun. Now I do their tours whenever I'm there. This trip I'm doing 3 different 2 hour tours.
Hope you have a good time!