Hello Robert! Welcome to the Disney Parks Moms Panel.
As far as proximity to Disney's Polynesian Village Resort, both Fantasia Gardens and Fairways Miniature Golf, and Winter Summerland Miniature Golf are still a couple of bus stops (or quick Minnie Van) away.
Fantasia Gardens and Fairways Miniature Golf is the closer fo the two, located close to the Walt Disney World Swan Hotel. To get to Fantasia Gardens and Fairways Miniature Golf using
Resort Transportation, you will have to take a bus to Disney's Hollywood Studios Theme Park and then take a Friendship Boat or bus to the Walt Disney World Swan Hotel. You could take the monorail to Epcot and walk through Disney's Boardwalk Promenade to the Walt Disney World Swan Hotel, but this is longer and requires Theme Park Admission to cross through Epcot.
Getting to
Winter Summerland Miniature Golf is the same transportation route as visiting Disney's Blizzard Beach Water Park and requires a bus trip to Disney's Animal Kingdom Theme Park followed by a transfer to
Disney's Blizzard Beach Water Park. Winter Summerland Miniature Golf is located beside the Water Park.
While navigating to the Walt Disney World Resort Miniature Golf courses is doable, the most direct route is through private transportation using your own vehicle or the
Minnie Van Service (which comes with a fee).
Have a Magical Round!
~Todd