I would imagine that it depends where you put it. If I remember correctly, I think the one in Orlando was like $600 or $700 (don't quote me on that). I'm pretty sure that there's some billboards on New York Ave. in D.C. near the XM headquarters, but I don't know if they're available.
Most billboard companies offer special rates for what are termed temporary marketing campaigns. these allow you to rent boards for 1-3 months, or rent boards on a temporary or rotating basis. I used to advertise through them in alabama/mississippi. I usually had 1-3 boards at any given time and they were boards that were either not currently sold to someone else, or between permanent advertisers. Often these were as little as $500 per month, plus the artwork.
I don't want to rain on the parade, because I love this idea, but a billboard in the NY metro area will go for tens of thousands of dollars. Probably in the 40-50 grand range for a month. Not sure if they do them for shorter intervals.
I'm a professional graphic designer and would be MORE than happy to donate my services to put the billboard(s) together. I think an important thing would be for them to look really professional... there are ways to design things nicely and not use logos illegally. If someone out there wants to take care of the details (what the billboards should say, dealing with the companies for distribution, getting proper templates to use, etc. etc.) count me in!