I don't know about any youth hostels. I have never been to Times Square on New Year's Eve, but some pople I know have been. It is usually freezing cold and you are surrounded by throngs of people. Personally, I don't see the appeal. If you are still determined to go to Times Square, heed cash78mere's advice. Don't bring or drink liquor outdoors because you can get ticketed or confiscated or worse. I will be warm indoors having a Rocking Eve with Dick Clark.