Some kind of high-end hiking sandals that have treaded rubber soles, leather insoles, and strong leather straps with velcro fasteners. I got 3 pairs many years ago at Mountain Equipment Co-op (Canadian chain). They're my normal, everyday footwear all summer so I'm completely used to them. I can walk and stand on them for hours. The soles are almost 1 inch thick so you can walk through small puddles and not get wet.
The only drawback for theme-park touring is that if they get wet the leather insoles feel slimy and it takes them a while to dry out. To avoid this when riding on raft rides, I take them off and slip them into the waterproof compartment with the hats and fanny packs. Cast members don't like this because they want you to have shoes on in case of an emergency evacuation, but we do it anyways!