I do a LOT of hiking in my free time, so I wear the same shoes at WDW that I do any other time I'm not at work - New Balance 481 all-terrain running shoes. The only downside to this is wet feet if you happen to be there on a rainy day (there really aren't any rides at WDW that will get you that wet) and I've lucked out and seen little to no rain in my last few visits.
I personally couldn't handle wearing sandals, even athletic sandals like the Keen ones, for 25K+ steps of walking. But my wife does the same 25K+ steps in flip-flops, so your mileage may vary.