After doing this instructable , I wanted to make it a completely clean look by eliminating the HDMI cable and the power cable. The plan was to install a new power outlet behind the TV, and install 2 (not sure what they're officially called) media boxes, which let me pass the HDMI cable (or any other component cables) through the wall.
Disclaimer: this instructable involves, among other things, messing around with wires in your wall. I am not an electrician. I've done a lot of light fixtures and ceiling fans on my own, but I never have anything inspected by a professional. Though everything functions as intended upon completion, I might have done something incorrectly. Feel free to correct me, or add tips for other people in the comments below.