I just booked an apt at the Chalet Fontana in Muerren for April. They are not "officially" opened, so there is no food. I am looking for a place to have a nice dinner with a nice view in Murren, Gimmelwald, Lauterbrunnen or anywhere along that trail. We will be eating breakfast on top at the Piz Gloria.
Just across the street from the Chalet Fontana is the Staeger Stubli...it's not a fancy place, but definitely has good fun, wine, beer and a few tables outside but most are inside. If you step outside of the Chalet's apartment, turn left, walk 4 minutes you will find an EXCELLENT Asian Restaurant on your right. My kids lived on the chicken strips here. From the Chalet's apartment door turning right toward the Schilthorn Gondola you will find the Hotel Alpenruh which has a very nice restaurant. Again not a fancy place, but probably a step above the Staeger Stubli. Alpenruh also has a very nice dining patio with fabulous views.
There is also a restaurant in the Hotel Eiger which is supposed to be good - I've never eaten there. I think you will find more Hotel Restaurants than stand-alone restaurants.
Lastly, there's always the Coop grocery store which sells groceries as well as pre-made sandwiches, wine, beer, fresh veggies. The apartment has a small dorm-size fridge as well as stove/oven and dishwasher where you can cook with your ingredients from the Coop. Keeping some nice bottles of wine, juice, soft drinks in the fridge is a very nice plus.
Don't worry - you won't starve!