Rosh Hashanah is probably the most religiously oriented New Year’s celebration. With principles based on stories from the Torah (which is told in an incredibly entertaining and informative rap song, posted above).
It seems that the traditions of the holiday have somewhat merged with the traditional American celebration of New Year, meaning that the religious aspect has faded. Many Jewish New Yorkers no longer attend Temple services on Rosh Hashanah; they instead spend quality time with their families and save the Temple-going for Yum Kippur, the day of fasting which follows Rosh Hashanah.