West Iya and Mi-no-Koshi have the usual range of rice and noodle joints, all a bit on the expensive side by Japanese standards. Try grilled amego a local river fish at 500 yen a pop, sold by little stands here and there.
Many places advertise Iya soba noodles, but if you've ever been to another mountain in Japan you'll recognize the topping as the same sansai mountain vegetables served everywhere else.