If there is one dish, which you will definitely have to try, then that would be Bern's famous rösti dish. The base of this meal is grated potatoes fried in a buttered pan until they get a nice yellowish brownish colour and a crispy consistency. There are many variations of the rösti. You can have rösti mixed with nearly any kind of ingredients such as bacon or cheese.
A long time ago, farmers of the canton of Bern used to eat rösti for breakfast. Today it is not eaten anymore for breakfast but as a normal meal and has become the Swiss-Germans national dish.