Hello there,
Let's have a look at ticket prices without the JR Pass and find out the best option.
Tokyo - Takayama ¥ 14,710
(Shirakawago is traveled by bus)
Takayama - Kyoto ¥ 10,970
Kyoto - Nara (return) ¥ 1,420
Kyoto - Mt.Koya ¥ 560 covered (see details below).
Osaka - Tokyo ¥ 14,140
Tokyo - Nikko (return) ¥ 11,160
Tokyo - Kamakura (return) ¥ 1,840
For a total of ¥ 54,800 or ¥ 8,410 in savings as the 7 day JR Pass is 46,390.
Some notes for travel to Koya, the JR Pass covers the route all the way up to Osaka. From Osaka the last part is traveled on the Nankai Express which is not included in the JR Pass. The same applies when you travel back to Tokyo. First take the Nankai Express back to Osaka, from where the JR Pass will take you all the way to Tokyo.
As for the JR Pass, I think the 14 day pass is the best option. This because it covers all of your otherwise expensive travel and the JR Pass is also good for local travel in Tokyo and can be used as one ticket for all your travel.
Hope this helps!
Daniel
