Originally Posted by abmj-jr

If you are traveling on a Japan Rail Pass, there are direct Hikari shinkansens that leave Kyoto at 7:42am and 8:22am, taking under 2 hours to Hiroshima. If you are just buying tickets without a Pass, the Nozomi has more and earlier departures that take around 1h40m for the trip. If you figure taking the local train direct from Hiroshima Station to the ferry pier takes under 30 minutes and the ferry takes around 10 minutes, you could get to Miyajima by 10:30 or 11:00am. I don't have a ferry schedule handy but think it runs several times per hour. If you have a JR Pass, the Hikari shinkansen, the local train and the JR ferry are all included.

If you spend 4 hours on Miyajima, you would then be back in Hiroshima by mid-afternoon. A few more hours to see the Peace Park and Atom Bomb museum and get some dinner and you could catch an evening train back to Kyoto.