Have you been to Japan before?
If you go to Koya, visit Enryakuji too (is not open in winter) , is like 40 mins from Kyoto sta coming up from Shiga. Also Ise shirne and Izumo taisha are super special, quite unique and not at all like your normal temple complex.
I would not skip Osaka unless you have been there before.
For pretty castles, if you are into that, visit Himeji, Matsumoto castle are some of the most striking.
In Kyoto you should visit off the beat temples and what not. Not only you will see very few tourists but if you are lucky maybe not even anyone at all and they will be yours to admire without the crowds. For example, last week I visited Komioji, Biodojin and Taikokuji and they were empty.
Kyushu, well of course Fukuoka is a must but you dont need that many days there, Nagasaki is gorgeous and well worth the visit.
If you whant something more specific let me know. I highly recommend spend more and stay at ryokans if the area you visit have them.
If it is you first time there, visit the tourist places, they are quite beautiful, the castle of the Maeda, the gardens, etc. When you go to the Higashiyama area, visit the gold leaf museum, is small but wroth it and very close to the area and for what ever reason not many people visit it. Maybe consider since you will up there, to visit one day Toyama city, it was quite beautiful and close to Kanazawa.
