Inside the Tree of Life (It's Tough to Be a Bug theatre). It's a safe haven in case of tornado. I'm from Iowa, so as soon as we're in a tornado warning, my first instinct is to get under the ground, and Tree of Life is really the only option at AK.
At MK, Utilidors might be a good option (not opened to guests except in a Plan C evac, which we've never had before, as Hub mentioned). I'd also take the PhilharMagic theatre, anywhere within Pirates after the drop, and Ariel.
At Epcot, I'd stay far away from La Cava--all that glass everywhere would make me a little nervous, especially since La Cava isn't underground, it's in the pyramid above ground. I would probably seek shelter in one of the theatres, really any would do, including Soarin' assuming that the gliders are not running.
At Studios I would want to be in One Man's Dream or Magic of Animation.