I'd say stay at least 2 nights, maybe 3 in Muerren. There is more info at [https://muerren.swiss/en/ this web site]
[[File:muerren-lucerne.png|400px|right]]
From Muerren your trip leads to Lucerne - still in Switzerland. The train from Lauterbrunnen via Interlaken to Lucerne takes about 2:30 hours and is very scenic. It's best to take a Hotel along the lake, but that's pricey too (Lucerne is expensive in general, quite a few of the worlds richest people live here). I'd recommend the "Hotel Schweizerhof" for its nice views and being close to train station and everything, but it's not cheap. Avoid the hotels right next to the train station.
Once you're back, the downtown area of Lucerne has many shops and nice restaurants, it's really nice there. I'd say stay at least 2 nights, with an option for a 3rd.
[[File:muerren-lucerne.png|400px|right]]<br clear=both>
Depending on your time budget, you could go from here to Innsbruck in Austria (and to Munich from there), or go straight to Munich. If you decide to make a stop in Innsbruck, the train takes about 5 hours. A reasonable hotel is the "Goldener Adler" right downtown. If you're lucky, you may get the "Goethe" suite, a room where german playwright J.W. Goethe stayed on a trip before. Just enjoy the medieval downtown and the hearty Austrian cuisine here.