Hi, Ashley!
Disney's Polynesian Resort is a Magic Kingdom-area hotel, so to get to Downtown Disney (which is in the Epcot area) just head to the bus stop.
Walt Disney World Resort Bus Service will take Guests from the Poly to Downtown Disney, with two drop off / pick up points at DD. The first stop, Downtown Disney Marketplace, will take you closer to shops such as Disney's Days of Christmas, Ghiradelli Ice Cream & Chocolate Shop, the World of Disney and LEGO Imagination Center. The second stop, Downtown Disney Pleasure Island, puts Guests near both the West Side (Cirque du Soleil, DisneyQuest Indoor Interactive Theme Park, Splitsville bowling, AMC Theaters Downtown Disney 24) and Pleasure Island. All of these areas feature fantastic Quick Service and Table Service restaurants, too, so you'll never have to go very far for a bite to eat or cool drink.
Have a magical stay! Be sure to send more questions as you think of them, Ashley. We love to help!