I currently have mine in a new bedside table I recently got, it has a locking door. Before that I kept it in one of my dresser drawers, but it was farther from my bed than I liked. Which is where I usually am when I want to have it so it made sense for it to be closer, I also really like the security of the locking door.
Also I don't know why you couldn't freeze a pacifier, they're usually just made of plastic and either latex or silicone which should all be safe to be frozen