I would recommend something from MuxLab such as this -
http://muxlab.com/products/category/audio-video/stereo-hi-fi-balun-2-pack . The benefit here is because it is twisted pairs, you can run closer than you normally would to bad RF sources and not pick up as much, if any, noise to the signal. You will also be able to long distances without as much loss.
MuxLab has a lot of cool little boxes to fit a lot of needs for decent prices. I've used a lot of these over the years and they just plain work. They also have a great lifespan (they don't fail very often at all).
If you want to look at something a bit more sophisticated, check out the Stick-On line from Radio Design Labs. All sorts of mixers, BALUNS, amps, and more for a decent price.
BTW, in many environments like this, the owners of the place tend to go with an A/V matrix switch that can route audio & video to any TV from whatever source. Autopatch and Knox Video Technologies are the two I have the most experience with (we use them in a very different way however) but both run very well. More money than what your budget probably is, but worth looking into on EBay.
Good luck with what sounds to be a pretty cool little project!