Laplap,

http://www.gambo-ad.com/english/index.htm has a very nice list of accommodations in Miyama and allows you to make reservations directly with the establishment.

I myself have stayed at Ryoso Kawaguchi and enjoyed it very much, only caveat is that the meals here are not served ensuite (something which I enjoy immensely when staying at a ryokan). They have two baths and do allow you to lock the doors for private use. The location is just a block from the main street and the okamisan was very personable. If you are traveling during the winter season and enjoy oysters, the special all oyster course dinner is pricey (5000yen) but worth it.

It is very much worth the time to stay on Miyajima overnight. From dusk to dawn the town seems virtually deserted (a far cry form the huge crowds during the day), and you'll get to see the shrine and torii at both high and low tides (at low tide you can walk out to the torii). A tidal chart for Miyajima (in japanese) can be found at http://www.miyajima.or.jp/sio/sio047to12.htm Also Ikutsushima shrine is light up at night. In the daytime be sure to take the ropeway up to Mt Misen.