New York - New Year - how exciting!!! My daughter did it a couple of years ago and said Times Square itself is a bit of a no-no as they start camping out early morning for the best spots. All the streets leading into the area were closed off early as well but they managed to get access through one of the lower level streets and still managed to see the Ball drop
This link will take you to one of the bus tour companies which do the hop-on/hop-off services including a night tour - think is is $59 for a 72 hour ticket at the moment.
http://www.newyorksightseeing.com/tourpage.php?item=AL3
Not been to NY for a few years myself and think there are still quite a few places still struggling to get re-opened after Sandy - my recommedation would have been The River Cafe but don't think that will re-open for quite some time. Beekman Tower has a fabulous 360 degree view from its Top of The Tower restuarant where they serve breakfast, dinner, or you can just pop in for a cocktail which they serve from 5:00p.m. Sunday Brunch at The Peacock Room at the Waldorf looks amazing but have not ever managed to do it - next time though!!!
I am sure others will have lots of recommendations for you - you will be spoiled for choice!!!!

Have a wonderful time!!