Locals on Ishikgaki repeatedly told us to go to the Akaishi Shokudo restaurant in the northern part of the island. As a "shokudo," it served basic Okinwawan-style food including the local specialty "Yaeyama Soba" (similar to the more well-known Okinawa Soba). Also, as expected of a shokudo, the atmosphere was non-existent: stark interior, florescent lights, TV on in the corner. Most of the dishes include pork, so if you're a non-meat-eater, the options are slim (yes, the "Yasai Soba" -- vegetable soba -- does have meat).
That being said, if you're up north to see the Hirakubozaki Lighthouse around midday and you're hungry, there aren't many other options in the area. BTW, there is ample signage in Japanese that points you to the restaurant once you reach Akaishi (or here are the coordinates: 24.539474,124.300158).
Bottom line: One of the few places open for dinner in northern Ishigaki and convenient if you're visiting the northern point of the island. Probably not worth a special trip unless you're a real connoisseur of Yaeyama Soba.
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