2 week trip to Japan - advice needed re Itinerary and Rail pass please!

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Hi,

I'm travelling solo to Japan for two weeks in April and am wondering whether to get a 7-day or 14-day rail pass. And what my extra travelling expenses would be ie. trains not covered by rail pass.

My proposed itinerary is...

Day 1: Narita - Tokyo
Day 2: Tokyo
Day 3: Tokyo - Hakone
Day 4: Tokyo - Hiroshima
Day 5: Hiroshima
Day 6: Hiroshima - Kyoto
Day 7 - 10: Kyoto (day trips to Nara and Osaka)
Day 11: Kyoto - Tokyo
Day 12: Tokyo - Mt Fuji
Day 13: Tokyo - Kamakura
Day 14: Tokyo
Day 15: Tokyo - Narita

Also does this itinerary seem ok or is there something wonderful I'm missing??
Would greatly appreciate any advice!!

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