The Allmendhubel ridge above Mürren is a popular attraction. You get there by funicular train (a steep train pulled by a cable) that takes you from town, through a tunnel, to the top of the ridge. When you emerge at the top, you’re greeted with gorgeous views of the Lauterbrunnen valley, and Eiger, Monch and Jungfrau mountains. They have a very nice restaurant with large outdoor terrace, and an innovative children’s playground with swings and slides, but also water features and an underground tunnel (so they can pretend to be marmots).
Allmenhubel is also easily accessible from Mürren by foot, and the funicular train makes it easy to walk one direction and ride the other. It costs CHF 14 round-trip, and runs from late June until mid-October. This is a great easy day from Mürren, and a fabulous family activity. Take the gondola up, let the kids play at the playground, and have lunch at the restaurant.
When you’re ready to head back, you can either take the train, or better yet, walk down through the Blumental, passing the Sonnenberg inn (another restaurant possibility). This leads you to the “Children’s Adventure Trail”, more or less below the cables of the Schilthorn cable car, with an exciting zip-line in the woods, down to another playground and picnic area. It’s perhaps a 40 minute walk without stops, but there are plenty of places to stop and enjoy the flowers and beautiful views on the way down.
See the Allmendhubel page of the Schilthornbahn for details.
My absolute favorite area in the Alps is the Bernese Oberland, and my favorite stop is Mürren, a car-free cliff-side village surrounded by fabulous scenery. The mountains simply don’t get any better!