Since you are already staying in Munich and Garmisch, you are covering my first two recommendations. As far as a first place to spend a few days, Mrs. Anywhere and I would recommend Nuremberg. It has great train access from Frankfurt and to Munich, and is a great city to explore.

Garmisch is kind of an outdoor activity focused town. It needn't be strenuous outdoor activities. There are lots of easy, flat walks in the area, usually with a beer hall at the end! Other things we've done in the area include the Freilicht Glentleiten outdoor museum, Linderhoff Castle, Oberommergau, Andechs Monastery for excellent beer and food. But we've always had a car when we've been there.

From Garmisch, Mittenwald - the epitome of a picturesque town is a short train ride away.