What pass to purchase?

Hello there,

The 21 day JR Pass would be the best choice, given the amount of days you will spend in Japan and all the routes traveled.

Here is a quick breakdown of ticket prices.

Tokyo - Osaka ¥ 14,140
Osaka - Kyoto ¥ 560
Kyoto - Hiroshima ¥ ¥ 11,090
Hiroshima - Nagasaki ¥ 12,990
Nagasaki - Hakuba ¥ 24,500
Hakuba - Tokyo ¥ 10,000

For a total of ¥ 73,280 or ¥ 13,930 in savings as the 21 day JR Pass is ¥ 59,350. The JR Pass will most certainly give you more value as it can also be used for local travel within Osaka/Tokyo, to and from the Airport and in many other instances. It also serves as one ticket for all the above rail travel.

Hope this helps,
Daniel