The mountains near Garmisch have superb hiking, and you can eat or stay in the many "huts," some palatial, that are in the area. Make reservations here.

Schachenhaus - Access from Elmau

Reintalangerhütte - 

Zugspitze Tour

You can do a hiking/train/gondola loop that includes Zugspitze and the Reintal Valley, staying at huts along the way. It can easily be done in two days.