Kuraya Gallery offers accommodation when it's not occupied by visiting artists. There's a tatami room in the house, or you can sleep in the small wood-floored gallery room opposite. Both share the bathroom. The lovely owner speaks very good English and there is a small cafe attached (irregular hours) with breakfast for ¥500.
Kuraya is near Honmura Port, on the left if you're walking towards the Art House Project's Ishibashi installation.