MK - there are actually a few little hidey holes throughout the park, if it's not time for a show, we like to just sit on the fake grass in one of the squares in front of the castle. We also like to sit in the rocking chairs on the porch near the Hall of Presidents and I love to ride the Liberty Bell.
AK - I love walking the trails. There are a number of benches located throughout them.
HS - I like to go to HBD and grab a table and a glass of wine and maybe a Cobb Salad and relax. I used to love to roam the streets of America but those are gone now but back in the muppets area is pretty quiet.
Epcot - a number of the countries have peaceful places. The maze at the back of GB has benches, the garden in France, the garden behind the QS in Japan, the tile room in Morocco and the museum there, the garden in China, the waterfall area in Canada, the church in Norway - all are pretty peaceful and there are rarely a lot of people there.