NYE in NYC is an animal. Like the above poster said, Stubhub is available until 2 hours before the game. Refresh the page right before it closes and you can probably find a decent deal. Also set a price alert for the game. Sometimes people will significantly lower the price of their tickets to just get rid of them.
Regarding going out, MANY bars/clubs are ticketed for the night. Most are $100+ per person and will have some type of open bar and a champagne toasts at midnight. They are never worth the money you spend.
A lot of bars in the East Village, Lower East Side and Williamsburg are not ticketed. I suggest doing a bar crawl around those areas.
NYE in Times Square is a shitshow, like you said. Not recommended.