Unless you are a Celtic pagan (and they are out there so I don't mean to slight them) and a number of others, your New Year comes at the beginning of January. I have collected the phrase "Happy New Year" in several different languages so that you can either impress (or annoy) your friends, or actually use the phrase to someone who doesn't speak English. Although the Hebrew New Year is actually Rosh Hashanah (usually sometime in September), you can say "shana tova" at both New Years. For your Spanish speaking friends you can use "Feliz Ano ~Nuevo" with great gusto. What about if you know someone who speaks Irish? You can use "Bliain nua fe mhaise dhuit" but don't ask me how to pronounce it. The Celtic languages always seem to have too many letters to me. Then there are, of course, the French, they who have brought us champagne, brie, and French fries. To them I would wish a hearty "bonne annee" as I drain my glass and nibble on another escargot (with Brigitte Bardot?)
For our troops overseas, valiantly protecting our way of life, if you have the occasion you can wish one of the locals a gleeful "Sanah Jadidah" with a nod toward Mecca. And, to my wife's family on Sao Michael on the Azores (some of the best food ever, my wife's carne guisada will make a grown man cry) I would offer my heartfelt "Feliz Ano Novo"