Don't bother with any of the restaurants in the main high street area of Kitzbuhel, they are all very commercial at the expense of a true authentic experience. Walk the extra 2 minutes (yes, only 2 minutes) to the Eggerwirt to experience a wonderful experience.
This is a traditional Tirolean hut housing a hotel and a restaurant. The service was good and the menu very attractive. Hopefully you can get a table outside - weather permitting.
We had a great meal, the sautéed Chappelle mushrooms were a real treat! Quite different from the other Austrian restaurants on our trip - more variety.