My family recently spent one week at Hus am Bärg in Mürren, and I highly recommend it. The apartment is located very close to the cable car station (it is the first building down the hill from Hotel Alpenruh), but since it is not on the main street, it is very quiet.
The apartment has two bedrooms, each with two twin beds. There is a patio with wonderful mountain views over the Lauterbrunnen Valley. The kitchen is fully equipped, and there is a shared washing machine in the basement.
The owners, Fritz and Fabienne, live in the building, so it was easy to talk to them if we had any questions.