14 d pass?

we're planning a trip to Japan in May and have booked accommodation. Now we are onto the train passes. I think I did the sums and the 14 day pass seems like good value but just wanted some extra opinions (excuse any bad spelling). We are in Tokyo for a week prior to travelling around a bit. Our itinerary is:

Tokyo -: day trip to Nikko (get used to trains, escape Tokyo)
Tokyo to Hiroshima
Hiroshima: possibly Miyajima
Hiroshima to Kyoto
5 nights in Kyoto including trips to Nara, etc
Kyoto to Mount Koya
Mount Koya to Osaka
Osaka
Osaka to Tokyo

Many thanks