In my current theatre, we have a hidden 3/4 floor between floors (affectionately dubbed the 'Malkovich Floor') that is a remnant of the renovation. It is generally used for storage, but we have a couch there. It is warm, quiet, and the best place to go if you don't want to be disturbed. Since we work in rep and are pretty much always in tech or in performances, it is nice to have a place to rest between shows!
The oddest place I have slept (as many people did) was on the dryers in the wardrobe room. There was a whole row of them, you could put a blanket on top and have a comfy, warm nap between shows while the laundry was drying.