The Schiltorn (also called Piz Gloria) is Mürren’s local peak. At 10,000′, it’s relatively small compared to its neighbors, but the views are unbelievably grand. It’s crowded on sunny, high-season days and probably not worth a visit on cloudy days, unless you’re a really big Bond fan. You can check the monitors at the station before buying your ticket, and the James Bond-themed rotating restaurant on top is a bit outdated, but it’s still fun. It’s nice to sit with lunch or a drink and watch the scenery rotate by.
The Schilthorn cable car is a relatively expensive trip, but you’ll save 50% with a Swiss Half-Fare Card. Plan to spend at least an hour at the top, with 30 minutes to an hour travel time each way, depending on if you are coming from Mürren, Gimmelwald or Stechelberg. I have seen suggestions to take the cable car up and hike down, but hiking down is a dangerous plan unless you’re an experienced hiker – 5000′ down is a looooong way – and there are much easier trails near Mürren to try first.