Epcot's WS : There's that theater in Norway - you can get in through the gift shop. It's always quiet, the movie is soothing and relaxing, it's temperature controlled, and people come and go as they please. (It's at the end of the maelstrom ride). Also in the Timon & Pumba video/show thing... good little nap spot with comfy plush chairs.
HS - The pavillion for the Indiana Jones Stunt Show (in between shows), the beauty and the Beast Pavillion between shows (sit toward the back during shows, no one will bother you), grab a table outside the ABC Commissary in the shade. He'd look like he's holding the table while someone else is ordering/getting the food. Tower of Terror gift shop - there are benches in there. People will assume he's waiting for someone to get off the ride.
MK - The planters outside between the Astro Orbiter and the Tomorrowland Speedway. There are lots of benches and planters to sit upon there. Near the exit of Splash Mountain - people will assume he's waiting for people to get off the ride. Ditto for inside the Space Mountain gift shop - there are benches in there. Ditto again for the Haunted mansion gift shop. In the carousel of progress. Near Aloha Aisle. There are benches there too - great to people watch from, so I'm assuming napping would be nice too.