Is the JR Pass for us?

Hi Lucy and Gemma,

For this itinerary I don't think a JR-Pass would be the best option, this for a couple of reasons.
One is that reaching Mount Fuji is better done by Bus (from Shinjuku, Tokyo) then by JR and for Koya-san it is better to take a private railway company from Osaka.

Also with this itinerary your longest journey would be Tokyo/Odawara (Fuji) to Kyoto, which would cover about half the price of the JR-Pass, besides this however the other small trips you make simply don't add up to the costs.

Hope this answers your Questions :)
-Daniel

Thanks Daniel! Do you know the name of the bus company which goes from Tokyo to Mount Fuji?

Yes I do!

It is Fujikyuko Bus

Hope this helps!
-Daniel