This is a wonderful idea and I did not see it anywhere else : Next to Herzlisee and Brunnihuette you will find fire-grids at some places and you can buy coals, sausages and raw potatoes at a kiosk and grill them there.
Favorite Dish: Take with you whatever you like to prepare there on the grill in the open air or buy the ingredients at the kiosk that you forgot or that you did not want to carry with you
Brunnihuette is open summer and winter and it is the selfservice-restaurant next to Herzlisee. They have a large terrace with a wonderful panoramaview and some cosy rooms inside as well.
Favorite Dish: I had Kalbs-Bratwurst and Roesti, a very popular dish in Switzerland and mostly also the cheapest dish that you will find on a menu. Kalbsbratwurst is a sausage made of veal and roesti is similar to Hashbrown potatoes, but they taste best in Switzerland !
Schaukaeserei Kloster Engelberg is an interesting place, where you can watch how cheese is made and of course you will be able to taste some cheese there as well. They also have a well-sorted souvenir-shop and they even mail cheese to your homeadress - just click on the link below !
Favorite Dish: I had a plate with different cheeses of Switzerland, that tasted really great and the plate was 16,50 sfr (=10 euros). They have cakes as well and coffee, light snacks and you can sit inside, where you can watch the cheese-production or you take one of the many tables in the court of the monastery.
Try HOBELKAESE, they offer a good portion for 12,50 sfr (= 8 euro), it is a cheese that you can get only in Switzerland, very aromatic and you cant cut it, you have to shred it [shredding means hobeln in german]
There are quiet a few places to eat there but this Selfservice is for me more practical because the service is quick and offers a wide variety of foods,either international or regional specialties and it's also less expensive.