As others have said, I always alternate between two/three different shoes.
1. My top choice is the Ecco three-strap sandals (usually in black), which I alternate with running sneakers (that I buy at a running store). I've tried other brands that also worked well. The key things: a well-crafted footbed, adjustable straps (for when your feet swell), 'slip-on (more or less), water-resistance, and something that could be worn to dinner. My sandals aren't dressy, but are passable at most WDW dining locations.(better than sneakers!)
2. The running store I use is one that assesses the way customers walk before they make any suggestions. The place is super! They don't upsell, they give you the correct shoes for the way you walk/run. Insoles are also an option to improve the footbed of your running shoes.
3. RAIN! I also generally bring a third pair of shoes as well, because WDW is often VERY WET! The Ecco sandals tolerate mild rain, but they aren't meant for the kind of HEAVY DOWNPOURS WDW sometimes gets. But.. extra shoes take up too much luggage space...if I bring a third pair on longer trips, then they are often compact flip flops. Flip flops are good to wear to the pool, can double as slippers, and could be worn to the water parks.