I choose the Hans Christian Andersen fairy tale, "The Princess and The Pea". It's a short story about a young woman claiming to be a princess shows up at a castle for shelter one stormy night. Doubting her story, the queen of the castle decides to test the girl's story. The queen slips a single pea at the bottom of a bed of 20 mattresses for the girl to sleep on. The thinking is that a true princess is so delicate that she will be able to feel the pea and will not sleep well. The next morning the girl complains about a hardness in the bed that kept her from sleep. The castle rejoices and the young girl marries the prince.
I've got two folding ideas. In the first, the book cover unfolds into a circle--a shape of a pea. Undecided on the imagery to go onto the pea.
My other idea is that the outer book cover looks like a quilt folded over the top (much like when you're tucked in to bed). When you unfold the cover the inside poster will either have an illustration of the bed (with 20 mattresses) or be an illustration of a patchwork quilt that visually tells the story.