Berlin to Munich Six-Day Itinerary Advice

My wife and I will be travelling to Germany in August, landing in Berlin on a Sunday afternoon. We plan to be in Munich by Friday night and to stay there until our departure the following evening by rail to the Netherlands. We are very much hoping to see the best of what we can given our time constraints, with at least a full day on Monday in Berlin and a "must" visit to Schloss Neuschwanstein at some point later in the week.

We've been recommended a number of places to visit along our journey, chief among them being a stop in Bamberg. We're constrained to travel only by public transportation, which plays a big factor in to where we'll be able to visit.

Any thoughts or sample itineraries? Thanks in advance, everyone!