A couple of my favorite hideouts are:
1) The little corner next to the Fantasyland theatre. You can get a cold drink and a snack if you like. There's about 5 tables with 4 chairs each. Lots of shade and a little entertainment if the show's going on.
2) The Main Street theater is a nice cool stop for a 15 minute break. Normally quite empty and a couple of screens showing early Mickey & Donald cartoons, you can always grab a piece of carpet and snatch 40 winks)
3) The pier between Small World and Matterhorn is covered and has quite a few tables and nearby snack and drink available. This was closed a couple of weeks ago, so I'm not sure of it's current status.
Most of DCA is usually quite empty and there are some nice rest stops there if you need a break.
1) In Bug's Land grab a bench and watch the toddlers frolic in the sprinklers
2) Inside the animation building is a large open space (air conditioned) with large screens showing clips from classic Disney movies.
3) The Aladdin show, Playhouse Disney, the California, Golden Dreams & Muppet's 3D are all inside (air conditioned) with entertaining shows (in darkened theaters). Golden Dreams probably is the quietest of the bunch.
Also grab a spot in the shade for the Block Party Parade, take a quick cat nap and wake up to enjoy the efforts of a bunch of real hard working entertainers.