Be careful. The clearly marked "Vegetarian" dishes may not be vegetarian at all. The one that we ordered had naruto (fish cake) in it. When asked, the server lady told us straight-faced that it was fish. This made us suspicious that the "vegetarian" noodle soup may also contain fish broth.
We don't speak Japanese so we can't inquire further. But I would recommend avoiding any noodle soup dishes in this restaurant. The yasai yakisoba and yasai yakiudon might still be vegetarian. And the yuba sashimi is safe. But this doesn't make Hippori Dako more vegetarian-friendly than any noodle shop in Japan.