I think everyone has their own out of the way spot for each park...In MGM I like to just sit along Sunset Blvd or Hollywood Blvd. and listen to the music and watch the people running by.
In Epcot I like the garden behind the UK or sitting on one of the benches in France or Italy. Anywhere in the Oasis at AK is nice and cool...
In the Magic Kingdom my favorite spot is over near Cinderella's fountain...
Now you've got me wishing I was there right now!!
A great spot is in World Showcase. In Japan there is a small restaurant/lounge where you can get appetizers and shushi. Not to mention a cold beer or soda. It is located on the upper level down the hall past the main Benihana style restaurant. It is a great place to beat the mid day heat. It overlooks the seven seas lagoon as well the courtyard.