Hot feet are the worst. Makes me cranky and then I want to leave the park for a poorly timed break. I fantasize about putting my feet in the ice of some of those water bottle vendors.
So, what are the best QS with AC at each park where I can put my feet up for a few minutes. Shows are dark and cool but nowhere to prop up the barking dogs.
How about the People Mover.
Restaurants are definitely much more not the place to put feet up! I see feet up in a restaurant - QS or otherwise - and I am asking for a manager. Shoes are required for a reason!!
PM definitely helps a lot!
I would never remove my shoes or stick my feet up where people can see them in a restaurant. Yuck! I was more thinking putting them on a chair under the table. I would wipe the chair after (always have Clorox wipes in my Disney bag).
If you are at MK or AK, go on Splash or Kali River. At least if you’re wearing sandals or flipflops. Wet shoes might make it worse…
I am a Tevas in the park kind of girl thanks to the hot feet problem. Maybe I need to time my water rides better. Thanks.
I wore flip flops almost exclusively on my last trip in September, and found that just letting them dangle a little off my feet when I sat down helped a lot just because of getting a little air to cool them off. It was my compromise to not take them completely off 
Cooling foot spray with essential oils is amazing. If you’re not bothered by being the weirdo in the loo (no I’m not British but weirdo in the loo has a nice ring to it), you could pull your socks off one at a time and have a little foot breather with a minty spritz.
My sister and I started getting a cup of ice water at QS places and fishing out ice cubes to stick under our feet when wearing sandals. It feels amazing when your feet are hot and achy. Since you wear sandals, I’d highly recommend it!
Find out where the kid play fountains are, and try not to get the rest of you wet! I’m sure someone else here can help us out with their location, my kids have long since outgrown them. I’m thinking EPCOT has one, and maybe up in Storybook Circus at MK?