please seach " teshima-web" by google or something. this is official web site. and you can get information about accommodation.

Hello, I was in Teshima for only 1 day with a bicycle to explore the island. Sorry I can`t give you any advice for accomodation. Cordialement, John.

I'm aware there are a couple of lodging options at Naoshima island, mostly B&Bs and dormitory style places except upscale Benesse House; Check wikitravel. Also, only Benesse House guests are allowed to check out the oval part of Benesse House. I guess there would be some casual lodgings likewise at Teshima island as well. However, there aren't as many museums or artworks to check out in Teshima compared to the ones in Naoshima, you may want to spend more time staying over the nights in Naoshima, or try to cover Inuzima if you only have 2 days. You need to plan ahead weaving ferry schedules to different ports at both islands and museum open hours to utilize your limited time efficiently and effectively. From my experience, you only need half a day for Teshima Museum, and One full day for various museums and artworks in Naoshima. It'd be a great addition to participate in Open Sky Night Program at Chichu Art Museum if you'd be staying at Naoshima. (Reservation required at benesse artiste website.) Further, if you're a fan of Tadao Ando and would like to appreciate more of his works, you may want to check out Awaji Yumebutai, which is equally impressive and kind of on the way if you're flying from Osaka. Another Ando Tadao masterpiece Honpukuji Temple is also only a couple of kilometers away from Awaji Yumebutai. Good luck!