Hi,
I’d base in nearby Hall in Tirol. We stayed five times at the Gasthof Badl. A RS recommendation. Good central location.
www.Badl.at
Instead of the Zugspitze, a terrific mountain trip is right in Innsbruck.
https://nordkette.com/en/home.html
I know the Grossglockner Road was mentioned, but for a closer and even more dramatic and spectacular Alpine Pass drive, head into Italy and the Val Gardena. Less than a 2 hour drive and then drive the Gardena Pass.
If you’d like to stay on the “go”, I’d suggest a loop drive. We’ve done this in reverse.
Pick up car in Innsbruck. Head into the Dolomites to Val Gardena, over the Gardena Pass. Stay in La Villa, Alta Badia.
www.Montanara.it
Then head to and stay in Heiligenblut, Austria (at the southern start of the Grossglockner Road). Along the way take the Lagazuoi cable car trip (Dolomites).
https://lagazuoi.it/index_en.php
https://www.ederhof-heiligenblut.at/de/
Drive the Grossglockner Road, stop at Zell am See (very pretty alpine lake and old town) and wind up either in Salzburg or nearby in the Berchtesgaden area. Salzburg and Berchtesgaden are about 30 minutes drive apart). We’ve stayed five times in Ramsau bei Berchtesgaden.
www.Mayringerlehen.de
We also loved staying in Zell am See. We stayed at Pension Alpenrose. Parked the car and could walk to the lakeside promenade and old town in a few minutes. We rented a small electric motorboat for an hour on the lake. It was outstanding.
https://www.pension-alpenrose.at/
http://www.scheicher-boote.at/preise.html
Drive to Munich. Stop and tour Herrenchiemsee Palace along the way.
https://www.herrenchiemsee.de/englisch/tourist/index.htm