I'll share with you what I do to avoid soreness (as well as blisters, swelling, etc.). I do think it depends, to some extent, on each individual person's makeup, how they walk, what they do in the day, etc. Regardless:
1. An obvious one, I always ensure I have a high quality pair of running/walking shoes. I ensure that they're broken in before I head out for a Disney trip. I have done a fair amount of research, and the brand I almost exclusively use now is Hoka. Comfort unlike any other shoe I have worn. I also highly recommended On Cloud. Both of them, in my opinion, are far superior. I also recommend actually going to a running store to discuss what you're looking for...you'd be surprised what information helps guide you to the right shoe.
2. Another obvious one, but we take breaks when possible. We tend to go pretty high octane on our Disney trips, so it's important for us to rest when possible. Mid-day (or other time) naps, sitting for meals and just occasionally stopping and sitting to take it all in go a long way towards reducing soreness.
3. Tape. I generally tape certain toes together to avoid friction that leads to blisters. I have gotten them terrible before, discovered what was causing it and isolated those toes.
4. Callous/Other Spot Coverage. I swear by callous covers/pads. They reduce the stress on those parts of your feet and stay on all day. Do some research to see what kind/cut/variety you might need, but these help me a lot.
5. Socks. I think this one is overlooked, but I specifically wear socks that wick away sweat. Your feet can absolutely overheat and the direct cause can just as much be your socks vs. shoes. This is especially the case if you decide to use tape, callous pads or other items that require adhesive. You don't want sweat ruining it! I also recommend bringing a pair of backup socks too, in case Splash Mountain or other attractions take a toll.
6. Another silly one, but I also do a little stretching/warm up in the morning. Once certain muscles and areas tighten up, it starts to affect the rest of your body. I always try to stay loose and get a little stretch going in the morning
Hope some of this helps!