Just because I think this wonderful region of Germany needs to be more widely known (and I'm here now, in the same chalet hotel), I'm going to link my trip report from 2 years ago:
This time, I took the cable car above the Alpine level of the Nebelhorn, and continued my hike (with the dog) to the summit. It was a clear day, so I could see the Zugspitze to the east, the Alrberg massif to the south, and I think even the Berner Oberland to the far west.
I also paid a visit to Therme Oberstdorf for the first time today. Not nearly as elaborate as Therme Erding (what is?), but still a rather nice selection of saunas and thermal baths. Especially after a vigorous Alpine hike.
In summary... the Alps consist of a lot more than just the Berner Oberland, Dolomites, and the Chamonix massif. If you're headed in the direction of Switzerland from Munich, consider a stop-over in Oberstdorf. You could even use it as a mid-way compromise, if you'll have a car, between Lindau and the Bodensee to the west and Füssen to the east. You will not be disappointed.