The Alps are spread along Germany's southern border, but are fairly compact and easy to explore. Choose a central base and fan out from there. Garmisch-Partenkirchen and Berchtesgaden are the largest towns with the most convenient transportation connections.
Although the area is a popular tourist destination, the smaller destinations like Mittenwald, Ettal, or the Schliersee are quieter and make for pleasant overnight stays. For an unforgettable experience, try spending the night in an Alpine hut, feasting on a simple but hearty meal and sleeping in the cool night air.