If you really are having troubles getting a hotel room one of the two hotels in Starnberg (don't know names) should be quite cheap. They are right at the Starnberg S-Bahn station, not to be confused with the newer Starnberg-Nod station. It is a 25 ride from the center. The trains run every 20 minutes except after about 11 PM when they run fairly infrequently until 3, I think. If things are tough, it is an option. Plus you are right on the beautiful Starnberger Lake with the Alps in the background!