Hi there,
Lets take a look at your overall costs first:
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Narita airport terminal 1 > Tokyo: ¥3,140 (62mins, 79km)
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Tokyo > Nikko: ¥5,630 (121mins, 150km)
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Nikko > Tokyo: ¥5,630 (117mins, 150km)
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Tokyo > Kamakura: ¥2,100 (47mins, 51km)
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Kamakura > Tokyo: ¥890 (54mins, 53km)
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Tokyo > Kyoto: ¥13,420 (164mins, 513km)
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Kyoto > Nara: ¥690 (44mins, 41km)
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Nara > Kyoto: ¥690 (44mins, 41km)
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Kyoto > Himeji: ¥5,330 (68mins, 130km)
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Himeji > Kyoto: ¥2,210 (91mins, 130km)
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Kyoto > Hiroshima: ¥10,990 (112mins, 380km)
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Hiroshima > Miyajimaguchi: ¥400 (26mins, 21km)
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Miyajimaguchi > Tokyo: ¥17,850 (331mins, 916km)
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Tokyo > Narita airport terminal 1: ¥3,140 (58mins, 79km)
JR ticket cost: ¥72,110 for 14 legs
Please note that you will also be able to use the JR Pass extensively in Tokyo so you will also have additional savings there.
7 days vs 14 days + tickets
The difference between a 7 and 14 day pass is ¥16,800, so you'll need to spend more than this in addition to the 7 day pass for a 14 day pass to be worthwhile.
You'll certainly want to have the return from Miyajima to Tokyo in your validity period - at ¥17,850 this i more than the difference between a 7 and 14 day pass. Looking back 7 days from this period will take a 7 day pass from the 3rd to the 9th. The outstanding travel outside this 7 day period comes to ¥33,950, so I can certainly recommend a 14 day pass over a 7 day pass + separate tickets.
You can look up precise train timetables and costs at the Hyperdia travel planning website and learn how to use Hyperdia for JR Pass holders through our video blog.
Hope this helps!
