I'm just back and based on current closures and crowds, here's what I found that did and didn't work.
MK:
- the trail behind Tomorrowland Speedway that used to be great now contains a smoker every 5 feet. Even on a low crowd day, it was terrible. They started within 10 feet of the "no smoking beyond this point" sign.
- I second the 2nd floor of the Columbia Harbour House. I was there about 2:30pm and there were only 3 other groups on the entire upper floor. It was very peaceful
- There is a low concrete wall between Big Top Souvenirs and Pete's Silly Sideshow. It was partially blocked by a trashcan, but otherwise easily accessible. I laid down on the concrete for a 40 minute nap and while it certainly wasn't quiet, I was in the shade, mostly blocked from prying eyes, and it was calm enough to sleep. I did wake up to find an old guy sitting closer than he needed to given how empty the area was, though

- Hall of Presidents is currently closed. Too bad! That's a great place to escape to for a bit
AK: in addition to the paths listed above, I love to go to the Nemo show when I need to cool off and just sit/lay down. The show is rarely full, so I sit at the very back along the sides and often have an entire row to myself. I can either lay down, or just sit quietly.
DHS:
- The Beauty and the Beast show, like the Nemo show, is a good place to go to just chill out for awhile. It's not air conditioned, though.
- ABC Commissary's side seating areas were practically empty around 3:30pm. I sat there and charged my phone for a bit while I enjoyed a drink and air conditioning
Epcot: Morocco, Japan, China, the welcome center during festivals, etc