Advice if 14 day pass is suitable

Hi,

We are travelling as a family 4 to Japan for 3 weeks in Oct. General Itinerary below

4-10 Oct: Tokyo (plan to have day trips to Nikko and Yokohama)
10-12 Oct: Mount Fuji
12-15 Oct: Kyoto
15-18 Oct: Osaka
18-22 Oct: Hiroshima (including going to Miyajima Island and maybe Iwakuni)
22-26 Oct: Back to Tokyo

Based on my brief research I'm considering getting the 14days JR pass which we could use from initial Tokyo trip to get us to Hiroshima and take a flight back to Tokyo.

Do you have a better suggestion which could be more economical?