9 days in Japan

Hi!

I made up an itinerary for our 9 days in Japan, but I'm not sure if it's too rushed. Is it worth spending a day around Mt Fuju? Or would it be better to spend a day in Osaka (possibly with a trip to Nara?). Lastly, how does the itinerary match up with using a JR pass?

saturday: fly into osaka. train to tokyo.
sunday/monday: tokyo
tuesday: mt fuji: take early train there spend day & stay overnight (near hakone).
wednesday - friday: kyoto: take 3 hr bullet train from hakone to kyoto. spend 2.5 days.
saturday: hiroshima: two hour bullet train ride from kyoto. spend day & night there.
sunday: train to osaka. fly home.

(*Flying into Osaka rather than Tokyo because it's a lot cheaper from South Korea, our homebase)

Thanks for your help!