There's already an effort out there to encourage book-sharing via leaving books in public locations. It's called Bookcrossing. Apparently they've built a whole community where you print a sticker with a unique ID, and can then track it to see where it ends up. Apparently there are some places that are designated drops--might work to add, say, gate A1 at some airport or other. I'm not a member, but it sounds fun.

I have left books at hotels--lots of B&Bs seem to encourage that, with at least a shelf or two. Last one I stayed at in the States had an entire library.