...and if I were going to do what you are planning to do, without spending big on a hotel, I would get a hotel in Tarrytown, NY, which is an express stop on Metro North's Hudson Line, which offers full views of the River and Pallisades and is maybe 40 minutes or so north of the city and also a charming town to visit in its own right. I'd take the train into Grand Central, which is usually decked out beautifully on New Year's Eve, force my way into Times Square and then head for Grand Central afterwards.
That's how I'd do it if I was going to do it, and not stay at a hotel in NYC. I would probably start with the DoubleTree here:
http://doubletree1.hilton.com/en_US/...-York/index.do
The Doubletree offers advanced confirmed reservations for $177 per night.
And then Courtyard by Marriott here:
http://www.marriott.com/hotels/trave...wn-greenburgh/