I have to admit they closed down a LOT of our go to quiet spots!!! We used to love the ranch area in DL and would often find a quiet spot in Bugs land in CA. For now, here are our go to quiet spots:
DL: If we want a nice "cool" quiet spot we do Mr. Lincoln or Tiki Room. If we just want a quiet spot to chill we go to Snow Whites grotto, Tinker Bells area, the Island or Hungry Bear to sit down.
CA: Here we usually go in the Animation building and do a drawing or two, catch a Turtle Talk and wander around the library. Our outdoor go to is the Red Wood Creek (unless its being used for character meets.