Hi there!
For your trip the only JR Pass that will cover you outside Tokyo is the national Japan Rail Pass. Lets take a look at your proposed travel to get a handle on your costs:
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Narita airport terminal 1 > Tokyo: ¥3,140 (62mins, 79km)
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Tokyo > Nikko: ¥5,230 (121mins, 150km)
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Nikko > Tokyo: ¥5,230 (121mins, 150km)
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Tokyo > Kamakura: ¥1,700 (48mins, 51km)
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Kamakura > Tokyo: ¥1,700 (48mins, 51km)
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Tokyo > Odawara: ¥3,440 (35mins, 83km)
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Odawara > Kyoto: ¥11,550 (160mins, 429km)
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Kyoto > Nara: ¥690 (45mins, 41km)
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Nara > Kyoto: ¥690 (45mins, 41km)
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Kyoto > Hiroshima: ¥10,590 (112mins, 380km)
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Hiroshima > Kansai airport: ¥11,830 (166mins, 402km)
JR ticket cost: ¥55,790 for 11 legs
As you can see you'll make good savings with both options I think. As for which is better for you, it is hard to say. I think you have the following options:
- 7 day rail pass ¥28,300 + other passes while you are in Tokyo (eg Kanto pass, and Tokyo metro passes)
- 14 day pass ¥48,300
If your itinerary is fixed, then it will be worth looking into option 1 as you'll be able to make savings while you are in Tokyo, and then further savings when you leave the capital. If your itinerary is not fixed, and you think you may do a lot of travel in the first week, then you should look at option 2.
Based on your itinerary, I think in your situation I would go for option 1. You can purchase the JR Pass online here.
I hope this helps!