I'll take a stab at this so your question doesn't fall through the cracks.
Have we got the number of days correct ?This question is vague; I presume you are asking if your time allocation is good. Ultimately only you can decide this - it depends on your travel pace and interests. The biggest problem I see in your plans is Dec 2-7. Shirakawago sits in between Takayama and Kanazawa. The main village (Ogi-machi) you can see in just a few hours (and don't miss the mountain overlook over the place) - if you want to also go to smaller and less touristy places like Ainokura, then it will take more time. A farmhouse stay can be a great experience (especially after all the day trippers leave) but it is not cheap.
Takayama you can pretty much get through in a day. I recently got back from there, and it was honestly one of the few places I had a fair amount of time to kill after seeing a number of sights. The old streets are crammed with tourists and the shops are mostly selling tourist junk. I did see one sushi place with a long lineup though so it must have been popular and famous. The stories that some people are saying that it is just getting too touristy I can attest are true. But in the evening the place is a total ghost town. My wife got us lost looking for some restaurant she wanted to go to and we wandered over countless dark streets. We finally found the place on the most brightly lit up street in the whole area - and we were the only ones on the street (and the restaurant) - but the famous beef was quite good. For me, the Hida Takayama Folk Village was the most interesting place in the city - and if pressed for time, a good way to see what was, and skip Shirakawago if forced to.
Unless you travel very fast, Kanazawa is likely worth more than a day. Seeing the Kenrokuen Garden is an absolute must.
The other big thing that sticks out for me is that whether you go to Koyasan from Kanazawa or Takayama, it is going to be a very long and painful trip.
Can we include any other towns ? It's up to you - but if I were you, I'd cut a day off of Osaka and go see Himeji.
What should we add to TBA days ?Lots of possibilities. Nikko and Kamakura/Enoshima are the first places that come to mind, but there are many more - Izu, Karuizawa, Kusatsu, the Boso Peninsula, Takao, Okutama, Saitama, and more. It depends on how far you're ready to go, as well as spend. Some rail passes like the Tokyo Wide Pass may save you some good money.
Should we consider Hokkaido ?It's possible - you can fly cheaply from Narita and get there in about 90 minutes on some low cost carriers like Jet Star or Peach.
http://www.jetstar.com/jp/en/homehttp://www.flypeach.com/pc/en or there is ANA's Experience Japan Fare.
http://ana.ms/20Xtf8tYou can certainly get away from the big cities, but if your main interest is autumn colors, you'd be way too late for that in Hokkaido. Did you see this site's page on
koyo?
https://www.japan-guide.com/e/e2014.htmlI'd say there are lots of great places much closer though, so save Hokkaido for a future summer trip.
