JRPass

Hi there!

That sounds like a really great trip to do in 3 weeks! Based on your timings, the best solution is to purchase the 2 week Japan Rail Pass + NEX/Suica deal I think (provided you do your Nikko leg within your 2 week JR Pass segment, if not, then a 3 week pass makes more sense). That gives you 2 clear weeks to explore the country.

The trip to Yakushima can be expensive and may be a little hard to squeeze in with your other elements, so as an alternative how about travelling down to Ibusuki in Kagoshima? Ibusuki is really famous for it's hot sand baths and great countryside so I'm sure you won't be disappointed. Another alternative is a trip to Mt Aso in Kyushu - you can learn more about getting to Mt Aso with a JR Pass here.

Hope this helps!