If I recall correctly, Vol 3 of Liminality took place in Hida, Takayama. I had the pleasure of visiting this small town myself this summer. It truly is beautiful, however I wasn't able to track down the locations mentioned in Liminality, mostly because I lost the 3rd OAV. That aside, its very similar to the anime: lush, green forest everywhere, surrounded by mountains. If there is any interest, I would be happy to post the pictures I took there.
It was one of my favorite places in any anime, and it was even more enchanting in person.