The "Art Island" of Naoshima is best enjoyed at a leisurely pace, with its range of museums, outdoor sculptures and other sights; so while it's possible to visit as a day trip from Okayama or Takamatsu, it's better to stay for a night or two and allow yourself the time to, well, take your time. When I visited, I decided to stay at a small guesthouse called Yado 7 Beach; just up the road from the 007 Museum, a few minutes' walk from Miyanoura ferry terminal, it's convenient for buses to the other side of the island, the I Luv Yu art onsen, and the town's small range of restaurants and cafes. While not luxurious, it's inexpensive, welcoming and perfectly comfortable.
Having arrived on an early ferry from Uno on the mainland, I left my bags with the friendly English-speaking proprietress (once I'd telephoned to ask her to drop by) then went off exploring the island, and came back to check in later. My room was compact, pretty simple but very clean, with a cool-underfoot tatami floor - some of the rooms are carpeted, but I much prefer tatami - a small LCD TV on the wall, and an alcove, small table and rail for my luggage and clothes. I slept on a futon laid out on the floor, which was warm and comfortable enough for me to get a good night's sleep.
Other than the rooms, there's not much by way of facilities. None of the rooms are en-suite, with shared toilets and bathroom (though I indulged at I Luv Yu in the evening after dinner). The small lobby has a TV, microwave, and a few folders with information about the island, and there's also a rice-cooker, free tea and coffee, and washing machines outside. The booking website I used says that no meals are served, but their own website gives prices with no meals (¥3,600-¥4,200 per person), with breakfast included (¥4,500-¥5,100 pp), or with two meals (¥6,700–¥7,300 pp).
I didn't actually spend much time at Yado 7 Beach as I was mostly out and about on the island, but it was just what I wanted - an inexpensive, friendly and well-located place to stay for a night in reasonable comfort.