If your destination is Salzburg, Garmisch-Partenkirchen and Mittenwald are a little out of the way. The Zugspitze is the highest mountain in Germany, and it's thousands of feet above Garmisch, but it's not a really high mountain (the top is below the parking lot where I used to ski in Colorado).
There are lots of aerial lifts in Germany. A very beloved mountain in Bavaria is the Wendelstein, which although even lower than the Zugspitze towers above the surrounding valley. It's more on the way to Salzburg. There is a Seilbahn (cable car) from Osterhofen, which is about 1h15 from Munich on the Bayerische Oberlandbahn, near Schliersee. You can ride to the top of the Wendelstein, then go down the Zahnradbahn (cog railroad) to Brannenburg on the Inn and from there to Salzburg via Rosenheim. Or, you could come back down the cable car, then take the train, 3 minutes to Bayrischzell. I saw this place, Alpenrose, when I went through Bayrischzell and thought it looked like a nice place to stay. The next morning, take the bus, Wendelsteinringlinie, over the mountains via Tatzlwurm to Oberaudorf and the train from there to Rosenheim.
If you want to see an authentic castle, take the train from Rosenheim via Muhldorf to the castle at Burghausen.