Stage destructibles range from houses, boxes, stalls, and trees; if it exists within the playable field, it can most likely be destroyed. Some exceptions exist if they do not give to you punching at them, but you will easily obtain this through your run through the Dramatic Log. To help you get a picture, without going out of my way, I obtained this during the Water 9 / Enies Lobby Arc of the Dramatic Log. If you still don't have this by the time you've beaten the Dramatic Log, you've gone out of your way to avoid property damage and you should be congratulated, but beyond that, take part in the Treasure Log and go out of your way to destroy innocent objects.