If you are there while BTMRR is still being renovated, that back corner is actually pretty quiet most of the time. there is even some games to play. Don't go too far though, the very end of the walkway is the smoking section.
I usually like taking a break on the seats near the restrooms that are next to pirates. that little are is usually just people passing by as there's not much else there. Also the food place (I can't remember it's name) directly across from pirates is only used when it's very crowded in the park. A lot of the seating has no ropes or anything to stop anyone from sitting down and taking a break. very few people do but some take advantage of it.
There is a tree that's on the path just before you get into adventureland coming from the hub.. This used to be a smoking section but now that it's not it's rather quiet. There is seating around the tree so you can sit with minimal things to see and stimulate you.
Hit or miss on this spot, but the gift shop at the end of space mountain (you don' thave to ride to go in it) is a charging station so there is seats and outlets along one of the walls. If it's a rainy day or really hot it tends to be a little hectic but when it's not it's very quiet in that back corner.
first aid and the baby station are both quiet. In mk it's located between casey's and crystal palace next to the rest rooms. I don't remember if first aid has seats in this park. First aid in epcot is like a lounge that nobody knows is there and animal kingdom about the same.
Other than that, if you do need to leave, contemporary is top of my list with quiet and comfortable seats on the first few levels. just stay below level 4 where the shops and food is. Of course if you need a few hours of break, head to your room, freshen up and relax there.