Cheap Method for Audio/video transmission in a building
There are two options, neither of which is particular expensive.  You can either use a component cable with a distribution amplifier or if you prefer a digital signal, there are wireless HDMI transmitters that will also work well.  

A distribution amplifier and a repeater are essentially the same thing, just slightly different purposes. A distribution amplifier boosts the power of an analog signal to account for the attenuation when sending it over one or more lines or a long line. A repeater is similar, it reads the signal in on one side and outputs it again on the other. The main difference is that the repeater will reduce line noise since it is interpreting the signal rather than just boosting it.

You could try doing a wired HDMI, but it would likely be quite pricy.
HDMI is a digital signal that is designed in such a way that it doesn't handle long distances well on the wire. Currently, the effective reliable limit for an HDMI cable is about 10 meters. To make a 50 meter run reliable, you would need 4 repeaters and 5 10 meter rated HDMI cables. This is going to be far, far more expensive than a wireless HDMI unit that is rated for even twice the distance.

You could try just using a 50 meter cable and hope that your hardware on each side is powerful enough to make sense of the data on the line, but I wouldn't expect it to be a reliable connection if you use a physical HDMI wire without at least 2 or 3 repeaters minimum. 

So for reliable solutions, you can probably do the analog wire &amp; distribution amplifier solution for about $150 or the wireless for about $250 to 350.  Putting a DA on both sides of the wire solution would allow for you to choose which way you wanted to send signal by plugging in the DA on that side.