I had a great time in NYC over New Year's.
If you're pretty much a complete tourist like I was, I recommend the Top of Rock observatory. It's just a 70 floor building that sends you to the top for some great views of Central Park in one direction and the Statue of Liberty area in the other direction.
They sell the observatory tickets along with an entry into the Museum of Modern Art for $30... not a bad deal.
Other than that, I did a lot of wondering around Central Park, went to the NYC public library as per this thread's recommendation, MoMA of course, and had a great meal pretty much everywhere we went. We also went to some trendy Italian dessert place which was pretty good. We spent New Year's eve in a club called Pressure... it was pretty awesome. Like $150 for a table and bottle service (we bought the VIP tickets well in advance). It was busy enough to have a good environment but it wasn't packed like I was worried it would be.