First time visiting Japan

Hello! My future husband and I will be visiting Japan for the first time on our honeymoon in October. We are debating getting the JR pass and if it makes sense with our itinerary, and if so should we do a 7 or 14 day pass. Any information is appreciated!

10/4: Travel from Haneda airport to Tokyo
10/4-10/9: Tokyo stay with 1 day trip Mt. Fuji
10/9: Travel from Tokyo to Kyoto
10/9-10/14: Kyoto stay with 1 day trip to Nara
10/14: Travel from Kyoto to Osaka
10/14-10/16: Osaka stay
10/16: Travel from Osaka to Hiroshima
10/16-10/17: Hiroshima stay with 1 day trip to Myajima
10/17: Travel from Hiroshima to Tokyo
10/17-10/19: Tokyo stay
10/19: Travel from Tokyo to Haneda airport