I'm going to say the most relaxing "ride" is the boat ride that goes between the Contemporary, Fort Wilderness, and Wilderness Lodge. It's sunny, it's windy, and it's just a nice relaxing boat ride.
I am surprised Epcot has not been mentioned more, Epcot has the most rides that fit into this category with Spaceship Earth, Ellens Energy Adventure, and Living with the Land all as top contenders! As far as MK, I agree that TTA is a good choice but to be honest is hard to find any areas of MK that are "calming" considering how crowded and hectic the park always feels.
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