Hi, Carolyn!
I completely understand about not wanting to pay for transportation while in Walt Disney World. If there is a way to get from point A to point B via WDW's complimentary transportation, then that's the way we're traveling.
If you're staying at Disney's Polynesian Resort, then either walk over to the Transportation & Ticket Center (if close enough to do so) or take the monorail to it. From there, you can take a resort bus to Disney's Yacht Club Resort. Keep in mind that once you have finished breakfast, you can take a leisurely stroll or boat ride to both Epcot and Disney's Hollywood Studios. You might want to plan a day of touring one of these two parks that day, heading back to the Polynesian Resort at the end of the day.
Take a look at this
map of Disney's Yacht Club Resort to see how convenient it is to go from there to either park. Zoom in a bit to see the boat dock as well as the walking paths to each theme park. Of course, the entire BoardWalk area is so beautiful, you may find yourselves touring there for a bit before you're willing to leave. :-)
Send more questions as you think of them, Carolyn; we love to help!