14-16 days first time visit

I would like to ask for your opinion and suggestion about my itinerary.
I have started my research and planning our first trip to Japan for 14 to 17 days (flexible)
It will be two (my husband and I) or four people (our two daughters, in their early twenties, if their exams allow).
Time: late spring - early summer 2020
Our flight will be from Toronto to Tokyo and we want to explore South Korea after Japan (depends on $)

My rough outline for our trip in Japan:
Day 1 - Afternoon, arrive to Tokyo - 1st night
Day 2-4 Tokyo (explore) - 3 days - 3 nights

Day 5 - to Hakone (...Mount Fuji) - 1 night (?) Overnight in ryokan /onsen

Day 6 - to Nikko (Toshogu Shrine...)
to Nagano - 1 night or (?) Overnight in Kusatsu onsen, or as close to Yamanouchi as possible

Day 7 - to Yamanouchi (Snow monkeys)
to Matsumoto (Castle)
to Takayama - 1 night

Day 8 - Takayama (Old town...)
to Shirakawago (village...) - 1 night (?) Overnight at a gassho-zukuri farmhouse

Day 9 - to Kanazawa (explore)
to Kyoto - 1st night

Day 10-12 - Kyoto (explore) - 3 days - 3 nights

Day 13 - to Nara (Castle)
to Koyasan - 1 night (?) Overnight at a Buddhist shukubo temple

Day 14 - to Himeji (Castle)
to Miyajima - 1 night (?) Overnight flexible

Day 15 - Miyajima (explore)
to Fukuoka - 1 night (?) Ferry to S.Korea, overnight if possible

Day 16 - to Busan, South Korea

We want to experience Japanese culture (cuisine, ryokans etc) and explore as much as we can.
Any tips and suggestions of what I should change, reconsider or add will be very appreciated.
Thank you

Day 7 and 14 are not realistic. Lots of time in transit.

You need to loosen your schedule a bit, especially on day 6 to 9 (or otherwise you will be forced to do so anyway by the time of your trip due to time constraint). Not every city has train or bus connections as convenient as Tokyo to help you move around quickly, and some don't operate at night.

you stay in 10 different hotels, what means you loose a lot of time on looking for hotels, checking is and out. Trip is much more enjoyable, if you choose 4-5 places where to stay and do daytrips.

I thought writing down the days that sound irrealistic but it is really most of them. Except Tokyo and Kyoto.

I admit being a slow traveler though.

Note that my Fuji hiking season is in the summer only. This webpage here has the details. For hiking it you would also need to allow an entire day at least.

Enjoy planning your trip to Japan!

If you do some research, and note down the travelling times you've got planned for each of your days, you might see where people are coming from when they tell you your itinerary is too rushed.