Just to add to the above--
In addition to the 2-gang (Or 3-gang, if you want more room) conduit above holding the RPi or BBBlack, You can put another 1-gang box right next to/below/above it, and put a 6 port keystone cover on.
You can get keystone inserts for a variety of cable types, including USB, RCA, HDMI, COAX, and pals. This lets you cleanly and aesthetically terminate cable connectors to the wall behind the TV.
The rPi is powered by USB power, and needs a 2A power source for full draw (assuming you have lots of things hanging off the USB port). There's generic devices that can service this need quite robustly that can be embedded inside the housing receptical. A 3-gang enclosure gives another 2 inches on the long side, allowing for a powered USB hub in there. This hub can power the rPi, and provide some additional ports.
If you dont mind lots of junction boxes in the wall, Here's a perfectly workable arrangement.
Box 1: 3-Gang conduit with metal top. Houses the rPi, and has some room for any extras you want.
Box 2: 2-gang conduit with ivory keystone plate top. Houses a compact USB hub and a USB video capture device. (video for linux compliant) Cables are routed into this box from the rPi in the 3-gang box, and has keystones installed for HDMI out, RCA out, Stereo RCA audio out, RCA video in (capture device), stereo RCA audio in (capture device), ethernet, 3 USB, and one blank keystone modified with a momentary push button.
Box 3: Deep style 2-gang, metal top. Houses an AC power outlet turned sideways so the plug faces toward studs in the wall. USB power source installed in this box in the remainder of space, routed to the rPi conduit.
Inside box 1, we have a simple interrupter circuit fed from the USB power source (say, a 4 port USB charger, with 2 ports being tapped. The first one supplies the VCC and GND for the rPi, fed through a magnetic relay switch. The second supplies VCC and GND for the coil on the relay, with the pushbutton between. When the pushbutton is pressed, the coil kicks on, and opens the circuit power going to the pi. when the switch is released, the coil goes dark, and the relay slaps back into place, and the pi comes back on again.) along with the rPi itself, and a little room to ziptie extra cable length.
Box 2 has an unpowered 5 port USB mini hub, and a compact USB capture device crammed in it. It gets fed by a single 6in USB cable going through conduit to box 1. The HDMI, RCA out, stereo out, ethernet and reset signal cables are routed from box 1 to this box as well. very short (do they make 3in USB cables?) cables connect the USB capture device's RCA inputs and the remaining USB ports on the hub with the keystones in the cover plate.
Box 3 supplies 2 USB cables from the power source to Box 1.
A loadout with XBMC for raspberry Pi, a low profile wifi dongle, a low profile bluetooth dongle, and a low profile USB stick plugged into the wall, and a bluetooth remote, and you have an in-wall DVR/HTPC.
the arrangement I see on the keystone plate looks like this:
RCA video out
RCA audio left out
RCA audio right out
RCA video in
RCA audio left in
RCA audio right in
USB 1 (wifi dongle)
USB 2 (bluetooth dongle)
USB 3 (hdd stick)
Alternatively, instead of RCA video and audio out, and if the capture device allows, component video RCA inputs, RCA video input, and RCA audio input on columns 2 and 3.
I dont know of any compact video for linux capable capture devices that can grab raw component that are USB though.