Being a vegetarian is extra challenging in Japan. This is a country where some restaurants think fish and bacon are vegetables as well. And although I believe the Japanese got tons of things right what we got very wrong in Europe, smoking in restaurants is clearly not one of those things.
Heianraku is a small restaurant, run by a lovely hospitable family where the atmosphere is great, you won't be gassed to death while enjoying your dinner and which serves tasty food (vegetarian if you wish) for a very reasonable price.
We went there twice and loved it.
If we ever come back to Takayama, we'll make sure to have dinner there.