If you go to one place in Takayama, make it this one. The food is excellent and plentiful, there's an English menu, the setting is very nice (at the bar or on tatami mats), but most of all the owner Hiroshi is such as friendly and approachable person. She speaks English well and is very interested in other countries, so it was great to chat with her about our own culture as well as Japanese culture.
I think there's place for about 15 people, and initially when we wanted to go in there was a sign outside saying it was fully booked. Fortunately for us some people just left and were able to enter. If possible I'd advise making a reservation in advance.