I would explore the resorts, especially the non-monorail ones, since it's hard to make time for them on a busy theme park day. Take a stroll at POR, watch the animals at AKL, hang out by the fire at WL.
Of course I would get in some monorail rides as well.
If I were to think of what to do at the parks, I tend to think of things that would be gray areas of the rules. What count as rides? I very much enjoy Tom Sawyer Island and the HISTK playground. You can enter The Seas without riding with Nemo and Friends. For that matter I assume you can go backwards into any Epcot post-show, though only in the case of The Seas is the post-show really the main event. Other people have already mentioned shows, which as an attraction that is an experience with a set beginning and end seems to fall more in the category with rides.
Suppose anything designated as an "attraction" on the WDW website is off-limits. Then I would hang out in Mexico, my favorite environment of World Showcase. I'd spend some time watching the throngs in the Land. I'd walk the walkway past the Odyssey, and play with the fountains at Imagination. Yep, mostly I think of Epcot. There are some spaces I really like at the Magic Kingdom, like the train station at the entrance, Adventureland between the Tiki Room and Jungle Cruise, and Frontierland at the dock for TSI, but they don't encourage you to linger like you can at Epcot.
