Schilthorn
It is possible to take a cable car from Murren up to the revolving restaurant on top of Schilthorn. Fantastic views on a clear day.
In the winter season it is a very popular ski resort, with plenty of rental shops. It also has a few sled runs which are great fun.
Allmendhubel funicular - ride it up and hike down back to town
Rent mountain bikes from Stäger-Sport on the lower road - be warned the southern route to the valley has some rather aggressive single track of lose shale between Gimmelwald and the valley floor. Be prepared to walk your bike a good distance 30 min or so There is a nice restaurant in Sechelberg that is a nice place for a rest before the flat ride down the valley. You will also pass Trummelbach Falls on the east side of the valley. For the trip back up to Murren be warned We were charged and additional fare for putting our bikes in the cargo bin below the tram where people that carried there bikes into the cabin paid only the regular fair -
Via Ferrata Murren-Gimmelwald