In my living room there are built in, recessed drywall shelves/compartments. There are three ceiling to floor, and three rows across. They are deep and designed to hold entertainment equipment. The problem is that only one of the recessed compartments has a power outlet and cable connection. I would like to drill holes between the shelves so I can run cords down/over to the one compartment with the outlet. (I don't believe this is against code, in that I am not dropping cords behind walls.) The separating "walls" are only about six inches thick. I envision drilling holes that are about two/three inches in diameter and somehow capping them for finishing (e.g., a plastic donut shaped cap). I am not sure if that means running the cord through empty space, or through some sort of tubing. Does anyone have suggestions? Is there someting premade for a project such as this that I can purchase? Thank you!

 

Welcome to the forums! Using drywall caps is viable, but your hole should be square, not round so you can get a good fit. The caps don't bend well. HOWEVER, there are solutions. Go to Rockler.com who has quite a selection of decorative wire solutions.
Another thing you can do is utilize low voltage old work box rings. They are orange and you can get them at electrical supply houses or big box stores. Then you can use cat5 cover plates to run your individual cables through.
All this is assuming you will not be running from floor to floor, which you can't do and leave an opening behind the wall.