I like to plan a fun little game on AirBnB for this. Put in Europe as the destination, <$600 per month as the price, and a month as the duration. It'll show you available apartments in everywhere from Sicily to Northern Germany.
That is a most excellent game, problem is a lot of these are way out in the boonies. For instance I saw a beautiful place at a medieval Italian town for $28/day, its great! But I get the feeling there is nothing to do there after a couple of days so a month seems excessive. Could be wrong.