Apartments and holiday homes
If you stay for a week or longer an apartment might be a good alternative to a hotel room. The supermarket in Mürren allows you to get your groceries to do your own cooking. But, you'll also find several restaurants in Mürren. Some might be closed in low season though.
The landlord or rental company will provide a free Visitor's Card upon arrival. The card provides various discounts on local attractions and a few cableways. Note that if you own a rail pass, you will often get a better discount.
The e-domizil website offers apartments and holiday homes in Mürren and many other places. The best price is guaranteed.