Itinerary

Hi,
You can see regular fares, routes and schedules on Hyperdia.
Under "More Options", be sure to uncheck the Nozomi box since you can't ride that train using the pass.

I'd say with 3 weeks you can definitely fit in Yakushima. Of course you'd need to make a few changes. Since you are planning to see Hakusan, Kudoyama and Kamikochi, I'd say you can safely skip Kuju and use that time for Yakushima, plus it would help to add a day to get down to Kagoshima from Kansai. You could cut a day off of Takayama since you can see Shirakawago in just a few hours. Also be aware there is no rail to Shirakawago - you'll need to pay for the bus.

If you like hiking, some of the best hiking you'll ever take is along the way to Kagoshima - go visit the Akiyoshido Limestone Cave, which is a 300 million year old marvel 1 km deep with an underground river rushing past you and giant caverns - the best in Japan and simply stunning. Above ground there's also great hiking on the Akiyoshidai karst plateau. Fukuoka along the way has some good places too, particularly the Nanzoin Temple which is one of Japan's finest, yet almost totally unknown to the outside world. See this site as a good guide. And of course if you go down to Kagoshima, you should see some of it, especially Sakurajima and Senganen Garden.
For Yakushima, two good sources of info on transport and accommodation are Yaku Monkey and Yes Yakushima.

In Tokyo, If you want to use a subway, you might consider a 2 or 3 day subway pass. Kyoto is worth several days, but don't skip Nara either. You can see the best of Nara in about half a day by going to the Nara Park area. The Todaiji Great Buddha is a must-see, but also be sure to feed the deer, see Kofukuji and Kasuga Grand Shrine, plus two often overlooked gardens, Isuien and Yoshikien. After the temples of Kyoto close down around 5PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are wonderful.

If flying through Narita, one of the cheapest ways in and out is the 1000 yen bus.

Hi,

Thank you for the helpfull feedback and the extra tips to visite in Japan.
We will do a few changes in our itinerary.

But their is something in your feedback that I don't understand. You say we need to add an extra day to travel from Kansai to Kagoshima. With Kansai you mean the district where Osaka and Kyoto is situated?

Thanks,
Hylke

Hi,
The Kansai region includes Kyoto, Nara, Osaka and Kobe.

Good luck.