Arigatô-san

From the references in the film, it is not hard to infer this takes place in the mountainous southern end of the Izu peninsula (part of Shizuoka prefecture). The towns of Yugano, Kawazu-onsen, and Shimoda (mentioned in the film), are all in this area. The railroad (then as now) runs up the eastern side of the peninsula, so the bus is taking passengers from the relatively isolated western side across the Amagi mountains to the eastern side. From the configuration of roads, we can deduce that the starting point of the journey was probably the town of Matsuzaki.

In the film, this picturesque journey feels a very lengthy one. On the modern paved road, the entire trip today takes about 40 minutes by car.