If you're talking about the holiday December 31, then you use NEW YEAR'S with no article. If you're talking about January 1, you use NEW YEAR'S DAY with no article. If you're talking about the entire coming year, then you use THE NEW YEAR: "I'm going to my brother's for New Year's, then to my sister's for New Year's Day. I hope to see a lot more of them in the new year."

Thank you)

Anytime)))