If you travel on the JR pass, the itinerary below is a model.

Kyoto 7:49--(Hikari)-->9:35 Hiroshima 9:48--(Sanyo Line)-->10:13 Miyajimaguchi ( There are earlier connections.)

The ferry between Miyajimaguchi and Miyajima runs every 15 minutes, takes 10 minutes.

Miyajimaguchi 20:59--(Sanyo Line)-->21:26 Hiroshima 21:33--(Hikari)-->23:03 Shin-Osaka 23:24--(Special rapid)-->23:49 Kyoto ( last connection)

For schedule search: www.hyperdia.com/cgi-english/hyperWeb.cgi

If you can possibly swing an overnight stay in Miyajima - it's expensive, I would highly recommend it. We just got back from a trip to Japan, that included a 24-hr stay in Miyajima. I had fond memories of Miyajima, having visited there on a day trip as a teenager. Being able to stay there overnight, and getting to see it after dark (Torii and Itsukashima-jinja are lit up) and being able to walk around town in early AM light (before multitude of tourists show up) was awesome.

A day trip from Kyoto would be great too though. We hiked to the top of Mt.Misen and back in the heat of summer (lotta work!), but the ropeway would save a lot of time to cover most everything (it's a small place). It looks like the ferry runs late, so you could see most everything (even the Torii lit up, etc) and then return late late night to Kyoto, I think.

Don't miss out on Daishoin Temple. It's fantastic!