JRPass

Hi Alexandra,

A nice stop on the way back from Kagoshima will be Hiroshima/Miyajima, where you could do a good overnight without too much hassle (I especially recommend an island stay).

For Yakushima, it is possible in a day - I recommend the Toppy jetfoil service as the ferry takes a long time. Here's another post on a trip to Yakushima with information on the Toppy that you should find helpful.

Bearing this in mind, lets take a look at your costs assuming you arrive at Narita and fly out of Kansai airport:

1. Narita airport terminal 1 > Tokyo: ¥2940, (62mins, 79km)
2. Tokyo > Odawara: ¥3640, (35mins, 83km)
3. Odawara > Kyoto: ¥11750, (160mins, 429km)
4. Kyoto > Kagoshima: ¥23340, (296mins, 953km)
5. Kagoshima > Hiroshima: ¥18000, (173mins, 572km)
6. Hiroshima > Osaka: ¥10520, (109mins, 345km)
7. Osaka > Kansai airport: ¥3140, (57mins, 64km)

TOTAL: ¥73330 for 7 legs

As you can see you'll make minimum saving of ¥28,230 with a 14 day Japan Rail Pass so I can certainly recommend this option.

Hope this helps!