Benten Island, just off the beach on Shiraishi. You can walk to it at low tide.
The Moooo! Bar on Shiraishi Island will be open every day over Golden Week, from April 28 thru May 6. You can come out for the day (last ferry back to mainland is 5:42) or stay overnight and catch the beautiful sunsets from the beach!
Updated April 25, 2012:
There are room still available, however Amagiso is booked May 3 and 4, and the International Villa is booked April 28 and 29 and May 3,4,5. Villa reservations will fill up fast, so do reserve while you can. After the villa, there are plenty of places on the beach, the most popular being San-chans and Minshuku Harada. Amagiso is also popular, being the newest and cleanest place. It is located at the very end of the beach in a quiet location.