I've tried a wide assortment of shoes at WDW over the years. As others have said, slippery sandals pose a risk at WDW.
After many trips, here's my wisdom to impart:
You feet are an essential element of any WDW day. When they start to hurt, your day is pretty much done. Unless you are willing to limp or use a wheelchair.
Feet are a bit like other parts of your body, they can't be easily replaced. This is well known, yet plenty of people abuse their bodies until it is too late. (WDW is full of folks that abuse their bodies in assorted ways.)
I always bring two pairs of quality footwear to WDW, and alternate between the two.
In most months of the year, we typically alternate between sneakers and high quality sandals- the kind with ankle straps. There are a number of brands that meet this criteria, but it kind depends on the shape of your foot, how much arch support you need, and how damaged your feet are.
In summer, we tend to favor the sandals.
We do sometimes wear flip flops in WDW, (easy to pack, easy to get on/off, water tolerant) but generally only wear them around the hotel or (just) for water rides.
I've tried many sandals over the years. My current favorites are Ecco sandals. Technically, the black Babett sandal isn't waterproof, but I've worn them I the rain many times without any problems. Over the course of a day, your feet swell, and these shoes are adjustable. Several Ecco styles are also nice enough to wear to dinner, then back to the parks until midnight.
Whichever shoes you and your whole family chooses, make sure they are in good repair before you arrive! I've seen someone suffer a significant injury because their tread was worn and they hydroplaned on a puddle. I've also been with someone whose old shoe fell apart. Please, please do NOT wear old stinky sneakers! when it rains, and old sneakers get wet, the next-day stench is disgusting to everyone that has to sit anywhere near you!
