I'm usually one of those "gotta ride it, now now now!" people in our family. But I also really like lazing around the parks, especially if it's our 2nd or 3rd visit to that particular park during the overall WDW trip. We also try to have an R&R day on our trips, so I've got some personal favorite spots in some of the resorts I've stayed / or spent significant amount of time.
In the parks (people-watching mostly):
MK - I like the benches around TTA entry & exit. The rocking chairs in Liberty Square are good too (I think there's some in Frontierland too). Casey's is the place for us on Main Street. The benches near the 'Partners' statue are nice but may be more crowded than you might like.
AK - I like to relax in the Asia section of the park. There's a few benches by the monkey enclosure near the entrance to Kali River Rapids.
Epcot - Just about any bench in World Showcase, in those little areas winding off the main path overlooking the lagoon. My personal faves on the main path are the stone benches in China, the benches opposite the mini train garden in Germany, benches in France, and the benches in the England pavillion. I like to hang out near Test Track and near the fountains outside of "Honey I Shrunk the Audience". Also, (like Hugpug said), the central fountain behind Spaceship Earth is a good place to escape the hustle 'n' bustle for a while.
Studios - The dinosaur counter service has some tables - view of the Sorceror's Hat area, those are cool. The benches along Sunset Blvd. are nice, but they're usually in the sun. I like to hang out near Star Tours (I'm a Star Wars fan) to watch the kids dodging the AT-AT's water cannons. I also like to hang out by the Muppets fountain - there's always kids playing there.
In the resorts (more quiet / solitude areas):
Beach Club & Boardwalk - I like to grab a bench overlooking the lagoon and the Boardwalk itself. Any time day / night. At night you can see the Illuminations sky fireworks through the trees. Inside Beach Club, the Solarium & reading room are nice places to read the paper. I'm a night owl, so it's not uncommon for me to be hanging out at 2 or 3 in the morning with a book.
Wilderness Lodge - On the 5th or 6th floor there's a reading alcove overlooking the lobby atrium. Very, very pleasant place for a read or a nap. It's usually unoccupied (unless I'm there), but you can hear the activity down in the lobby. You can study the chimney very well if you're so inclined. This is my absolute favorite 'quiet' spot in all of WDW.
Old Key West - Behind Olivia's restaurant near the pool is a nice place to hang out. There's usually people around, so it's not a very good place to read.
Polynesian - Hang out in the lobby.
Contemporary - Hang out in the lobby. Watch the people heading to Chef Mickey's.
POP - Grab a table by the Hippy Dippy Pool. Grab a beer for me, if you don't mind...
yumm!
