September visit

We arrive in Tokyo in September, working on the itinerary but will be in Tokyo for 3 nights before climbing Mount Fuji, thinking about returning to Tokyo after the climb and departing the next day to Hiroshima then onto Kyoto, Takayama with potentially a day trip to Shirokawago then back to Tokyo . We are not fixed with the order of how we visit each place and open to suggestions but is it worth purchasing the JR pass for this itinerary?