I am wondering where to even begin to find a place that could print something durable like a 13' x 30' banner to go on the side of a building. Is this even possible? Is a vinyl banner the best option? What medium should I choose to cover the side of a 2 story building?
How long are you planning on having it up? If it's going to be permanent you're going to want to consider something that will hold up to wind and UV long-term better than vinyl (e.g., plastic / metal / wood). If the side of the building has windows you might consider vinyl graphics (of course, the people sitting in the rooms with the windows might not appreciate having their view partially blocked). There are also graphic options that cover windows but are transparent from the inside (you see these on buses a lot).
Vinyl is great if you are only going to have it up for short-term; you can roll it up and store it when you don't need it (don't forget to unroll it from time to time so the ink doesn't stick to the back of the sign) or if you're looking for portability. As far as printers, a quick google search yielded:
13' x 30' is pretty big - I wonder if there would be problems with the weight of the material pulling on the sign, particularly in a bad wind. Having never printed on something this scale I don't know if they would have to join several narrower printouts (I've seen 4' wide printers that print off a roll). I can't imagine this would be cheap, either.