Two Week Itinerary with JR Pass

We've scheduled Oct 18 -22 in Kyoto and then plan to take the train to Hiroshima and onto Miyajima for the night- of the 23rd - then the next two nights (24 & 25) we will stay with friends in Karatsu -then have until our flight from Tokyo on the 31st -- I'd like to visit Dogen Temple's, butit's far to Entsuji so maybe best to go to the Wakayama Peninsula and visit Koya -san and stay in a temple there. We'd also love to do some hiking -- Do we need to book Miyajima in advance? Wakayama, too - we're thinking it would be fun to jsut roam abit -- I speak enough japanese to get around easily. Any suggestions?

If you start a 7 day JR Rail Pass for Yen 28300 on the 23 Oct you can cover Kyoto - Hiroshima - Miyajima ( single ticket Yen 11 000 ) Hiroshima Kuratsu ( return ticket Yen 20 000 ) Hiroshima Kyoto ( single ticket Yen 11 000 ) any other JR travel ( for Koya san plus private railway ) till 29 Oct Kyoto - Tokyo ( single ticket 13 000 ). A 14 day JR Pass is Yen 45 100.