Roast pig is a must.  There are many ways to approach this, the best being getting a whole pig and then roasting it on a spit for many hours.  Seasoned with Adobo and Sofrito, with a cracklin’ skin.
Pasteles

Pasteles are similar to a tamale in form, but Puerto Rican in execution.  Made of a either a mashed plantain or cassava, they are stuffed with meat and capers and potatoes.  Then wrapped in banana leaves, they are boiled and served with white rice.  They are labor intensive to make, but are a marked tradition of the holidays.  
Coquito

Besides the Pina Colada, this is Puerto Rico’s most favorite drink, and is in fact our version of Eggnog, but without the egg-y flavor. If you are looking for a traditional holiday drink and are not a fan of eggnog, consider coquito, a coconut based ‘eggnog’. Coquito is made with egg yolks, rum, coconut milk, coconut cream, sweet condensed milk, cinnamon, nutmeg, and cloves. The drink is commonly associated with the Christmas holidays, where it is traditionally served along with other holiday food.
{https://caribbeantrading.com/puerto-rican-holiday-food-traditions/}

New Years

Puerto Ricans welcome the New Year surrounded by family and friends. Traditional food is served: arroz con gandules, roasted pig, pasteles, coquito, pitorro, rice pudding or tembleque.{https://www.geniuskitchen.com/recipe/coquito-puerto-rican-holiday-drink-for-christmas-and-new-years-193594}