We stayed at the RI SW over Christmas, and I would not have walked between any of your locations above. The roadway can be very busy and its just not pedestrian-friendly enough for me. The distance would be a fair hike as well....and when you are planning all that walking at the theme parks or waterparks, for us, adding a walk to and from the hotel would be wayyy too taxing.
The hotel offers a very convenient FREE shuttle to all locations that would be a safe and reliable alternative to walking.
Of course, YMMV!