Hi there,
My suggestion would be:
Day 1. Start in Tokyo, flying into either Haneda or Narita Airport. You can stay in Tokyo for this first day (or stay the day after as well if you wish) so that you don't have to use the pass yet. My suggestion would actually be to take your JR Pass exchange order to a ticket desk as soon as possible and set the activation date for when you need it to be validated, i.e. when you plan on leaving Tokyo for Kyoto. This allows you to start making reservations for your trips ahead of time to make sure that you are able to book the tickets you want, as this is a very tourist-heavy time in Japan.
Day 3: Tokyo --> Kyoto, spend time in Kyoto. In Tokyo you'll have a chance to see cherry blossoms, but there are also prominent places in Kyoto to see them as well, so the choice is yours, you'll just have to look into the specifics of what you want to do in each city.
Day 4: Kyoto --> Osaka, spend time in Osaka.
Day 5: Osaka --> Hiroshima, spend time in Hiroshima, it's worth looking into a trip to Miyajima Island; it's a very popular destination for tourists to make from Hiroshima.
Day 6: Hiroshima --> Shin-Fuji, you can take Shinkansen to Fuji directly and take your tour there.
Day 7: Shin-Fuji --> Tokyo
This itinerary accounts for only 7 days - you have the opportunity to include the extra day either in Tokyo at the start, end, or stay an extra day in one of the cities you'll be visiting, depending on where you want to stay longer.
Kind regards,
Alexis