If you are staying in a Disney Resort then you can go anyplace on site with no charge for parking. The water parks, the theme parks, restaurants, golf courses...anywhere.
I recommend doing just that. Disney transportation is some of the best in the world but it is so much more convenient and quick to just use your own vehicle. You may have to walk a few more feet to get to your car but you were going to be standing there anyway waiting for other transportation. JMHO