Please refer to train schedule : www.hyperdia.com
and ferry schedule: gethiroshima.com/features/…
Is it possible? Yes. Will I do these 2 same day from Kyoto? No.
1 way Kyoto - ferry dock for Okunoshima 3 hours . Ferry schedule does not always match up with the train arrival so you could be spending some time waiting for the next ferry.
It is not a matter of "best way", there is only one way to achieve, but a matter of checking train and ferry timetables and Castle open hours in advance, and acting as planed by all means.
If you are willing to start by 7AM and finish after 8PM, eat lunch on the train/station or at the park as fast as possible, then one day trip is doable.Edited: 25 February 2017, 16:13
If I were to do it (and I admit it sounds like an intriguing trip to try!), if you got to Himeji Castle at 9:00 when the gates open, you could possibly be on the 11:10 shinkansen, changing at Mihara for Tadanoumi, arriving by 1:17. You could take a later train, since the ferry leaves at 2:30. At the end of June, the sun sets at 7:00, which gives you plenty of time; you could actually spend another hour in Himeji and do Kokoen, taking the 3:30 ferry (there is a train that gets you there by 3:15, and it looks to be a five minute walk). Note that I've never been to Tadanoumi station or Okunoshima, and don't know what you're options are for food around there; but this could be an interesting adventure!
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