Here's my solution (I used to get them a lot too):
Wear
Crocs (only the name brand, not the knock-offs) Flip Flops. I can wear them all day, they have support and prevent my feet from sweating. In addition, if they get wet, they dry super fast.
And yes, I have taken them to
Disneyland, Disney World, San Diego Zoo, Wild Animal Park, Sea World, etc. Outside of work and church, they are pretty much all I wear. You might ask why, well, in addition to the reasons that I have outlined above, my knees (which are bad) hurt less when wearing them vs. other shoes. To me that is the best reason of all to wear shoes. Yes, I know they may not look the nicest to other people, but I hurt less when wearing them and find them more comfortable overall, so that is reason enough to wear them.
Just a warning though, you MUST break in a new pair by wearing them in places where you will not be doing as much walking as the places above before wearing them in the parks, or you will get blisters. I basically wear them for at least two weeks before taking a new pair of shoes into the parks.
There are many, many styles of Crocs, including many styles of flip flops, I have my favorites (which actually do have support in them, some don't), but everyone will have their own preferences. I am only letting you know what works for me personally. I am not trying to start a debate (which I know can happen when crocs are mentioned), just giving my advice for how I avoid blisters in the parks and since I go to Disneyland regularly (we live about 15 minutes away, yes it can take longer to get from the parking lot to the gate than for us to drive from our house to the parking lot, but that's another story), I definitely have had my share of blisters over the years and have tried many different kinds of shoes and overall, nothing has worked better for me. I originally tired crocs because of these forums, so I must say thank you for that.
Again, this is just what has worked for me, your mileage may vary, but considering you can usually get the flip flop styles (that have support) for around $15, it's worth a shot in my opinion.