Place the crate beside your bed with the open side facing towards the wall.
Measure the top of the crate, taking the measurements from inside the raised groove. Cut out a piece of sturdy cardboard according to your measurements. You can also use a piece of plywood if you want something stronger. Place the cardboard or plywood on the top of the crate. The raised groove should hold it in place and keep it from sliding around. This creates a smooth surface for drinks, alarm clocks and pictures.
Slide the crate away from the wall slightly and stock the inside with books, tissues, reading glasses and other things you would normally store in the drawer of your night table. Slide the crate back towards the wall to keep the things inside from falling out. When you need to take something out, simply slide the crate away from the wall a little bit and reach behind to grab it.
Cover the crate with a tablecloth or piece of fabric that matches your room decor. This disguises the fact that it's a crate and makes it blend in with the rest of your furniture.