Visit http://www.campingcheque.com/ (used to be called "CampingSpain.com") for some possibilities.

I recall reading - years ago - being legally able to set-up-tents on private property but I don't think that's done anymore. I could be wrong but I haven't read anyone doing this in quite awhile. Just finding the land-owners (if there's a lot of land, I mean) might be a difficult task but if you find them I hope you speak Spanish.

Might be more trouble than its worth, really, carrying all that stuff from place to place by car/bus/train, setting up, leaving it behind at a site while you're in the cities touring around. I'm not sure I'd feel comfortable doing that. Maybe you'd return to the tent to find a family living there and clothes drying on a makeshift line. hehehe.. Good luck!

Saludos, MadridMan