Over at Magic Kingdom at Disney World, several ride shutdowns could benefit you if the timing is right.
I once was given a pass to stand at the top of the Space Orbiter and watch the fireworks. It was incredible with a view most don't ever get to see, and a lot less crowded. If I were to get stuck on this attraction, or Dumbo, or Alladin, during the fireworks, I would be hoping that the ride doesn't start until the fireworks are over.
At EPCOT, getting stuck on Guardians of the Galaxy might be interesting given the visuals of the ride and maybe the music would play through all the songs...of course, sitting in a car listening to music isn't as much fun as riding through the attraction with them blaring.
Perhaps the best ride to get stuck on might just be Kilimanjaro Safari. There are no mechanics of the ride to stop it but the vehicles could break down and if you were stuck on a safari with wandering animals, it would be kind of relaxing and cool and the transfer to another vehicle could be interesting as well.
My personal favorite choice would be the Magic Kingdom's People Mover ride. If you get stopped for a long period of time in the dark, take a nap. Get stuck outside with a view of the castle, enjoy the fireworks. From above you can watch people and enjoy a conversation with the family. The ride is already relaxing and I tend to wish it was a lot longer so maybe the next time, it will break down and give me an extended stay!
Inevitably, attractions are going to stop. Did I miss one that would be incredibly fun to get stuck on? I can't imagine Nemo or Little Mermaid offer much in the department of enjoyment but maybe hanging over London on the Peter Pan ride might be enjoyable.