Arthur Laurents wrote a play that was literally called "New Year's Eve"
Oh, and there is a musical named Changes with a score by Addy Fieger, which chronicles the lives of a few characters in the timeframe of exactly one year, starting and ending with New Year's Eve. Larry Kert and Kelly Bishop were in the original Off Broadway cast in 1980.
In 1980, there was a Broadway musical entitled "Happy New Year" that lasted three weeks at the Morosco. It was based on the play "Holiday," in which New Year's Eve figures significantly.