With finishing The Mystery of Cabin Island (1929), and discovering that the book ends during the afternoon of New Year's Eve, I was trying to think of any other Hardy Boys book that takes place on or around New Year's. I know that there are a number of books where the story takes place in December, either prior to Christmas or going over Christmas, and ending just after.
I know that there is New Year's Evil from the Nancy Drew And Hardy Boys SuperMystery'88 series, which seems to take place from December 28 to January 1.
The Hardy Boys Casefiles #119 The Emperor's Shield takes place over New Year's Eve and New Year's Day, as far as I can tell. (New Year's activities get a mention in the first chapter, I believe.)
I think I remember a New Year party, likely from 119, since I have that book and must have read it in the past.