Mt Fuji & Shirakawa-go

Hi, we are a family of 5 planning a trip to Tokyo from 19 Dec - 31 Dec 2018. There are a few places we would like to visit includes :
1) Tokyo
2) Best view of Mt Fuji
3) Skiing
4) Shirakawa-go
5) Takayama

Can someone help to guide us for the itinerary. thank you

I cant help you with skiing unfortunately but our recent trip ticked a few of those boxes.

We went :
Tokyo - Lake Kawaguchiko (for Fuji views) by train from Tokyo Station. Bus is much cheaper, we just like trains when we are in Japan;
Lake Kawaguchiko to Matsumoto (train again). That isnt on your list but there is a castle so why not!
Matsumoto to Takayama - we went train and bus to Kamikouchi, Kamikouchi will be closed but you can bus all the way;
Takayama to Shirakawa-go - bus;
then I'd bus to Kanazawa, and train back to Nagano if you want to ski there. There is also some skiiing at Takayama.

By the way, look at Hotel Associa at Takayama. We have stayed a few times, it is a favorite of ours though it is a bit out of town.