A charming town between Hallstatt and Muerren

I can make two recommendations, but getting there would be impractical without a car. One, Lech am Arlberg. Beautiful little ski and hiking resort located high in the Tyrolian Alps, between Innsbruck and Liechtenstein. Coming from Hallstatt and going to Mürren, though, it might be a bit redundant. The other recommendation would be a slight detour into Germany. Lindau on the Bodensee. If there's a prettier view in all of Europe than looking out from the harbor to the distant Alps on a clear day, I haven't seen it yet.

Since you are traveling by train, what I would suggests that you input the route into a train website such as Bahn.de or SBb.ch, the Swiss rail website. As you probably know, it is a journey of around 11 hours so breaking it into two days makes sense. The route generally involves Hallstatt to Salzburg to Innsbruck to Zurich to Bern to Interlaken and on to Mürren. If you use the " show intermediate stops" function you will see that the halfway point is around Innsbruck, or maybe St. Anton.

Lech is what immediately comes to mind and I see has already been mentioned. So, another vote for it. Cute town in summer and winter.

Lichtenstein was a fun stop on one of my trips, but as Tom suggested not the most amazing place. However, the suggestion of the Lake of Constance (Bodensee) would be my choice as well. I have returned many times and it is such a beautiful and romantic place to visit, and I would go again in a minute.

Is there any way you can go from Munich to Hallstatt and then Hallstatt to Salzburg? At least then you won't have to back track on the next leg of your trip to Murren. We've enjoyed Bregenz and Lucerne - Bregenze is closer to your Austrian destinations while Lucerne is closer to Murren.