Mürren's après ski is generally cosy and relaxed with most of the hotels offering traditional stubli bars. A good way to start straight after skiing is with a 'cake stop' at the Bellevue. Later on there is music at the Tächi Bar and the Inferno whilst for night owls the Biemli Chäller should be lively through the night.
For a bit of a change rent a toboggan at a sports shop, take the funicular up to Allmenhubel then sled back down. Alternatively you can go down from Mürren to Gimmelwald and take the cable car back up or, if you want to work up an appetite, walk up to the Gimmelen restaurant, enjoy a meal, then toboggan back down to your hotel.