Bavarian Alps

I don't know of any towns in the Bavarian Alps that sit at a high elevation (not saying there aren't any, however). If you want a not-huge town with good amenities, I would look at Oberstdorf or the neighboring Kleinwalsertal, (a dead-end Austrian valley only accesible through Germany). Most of the hotels and guest houses seem family-owned. I've stayed a Hotel Filser a few times. Nice place, and a small herd of cows makes their daily commute to and from the pastures right by the hotel. It's kind of charming to watch.

Mittenwald meets the "mountain views, hiking, and hotel options" requirements. It's accessible by train too. Check out this old post about it:
https://community.ricksteves.com/travel-forum/to-the-west/mittenwald-day-trip-from-munich

DJ

I don't think anywhere can completely compare to Mürren, but there are few places in the German Alps that come close.

The Kleinwalsertal, as mentioned above, right outside of Oberstdorf, is an incredibly beautiful area, with bright green pasture leading up to rocky, snow covered peaks.

The mountains in Switz are more impressive and awesome, I have to say. But things are cheaper otherwise, and the mountains are still quite good. I assume you are flying into Munich?

In Germany look at Mittenwald and Garmisch. In Austria (near the German border) look at Schnaritz, Seefeld, and the towns around Innsbruck such as Igls, Patsch, Tulfs, Mutters, Natters, Götzens, Axams. The latter are all easily accessible by bus form the Innsbruck Hbf. The Stubaital is also easy access fro Munich, 2 hr train to Innsbruck and 30min bus to Fulmpes, Neustift, or Schönberg, you have some 3000m peaks here.