Itinerary advice please

Hi there, we are a family of 4 [two teenagers 15 & 17] travelling to Japan for the first time arriving on 29th December for 16 nights. We fly in and out of Tokyo.
We are planning on skiing in Hakuba for 4/5 nights from the 6th January. Other than that we would like to visit the Jigokudani Monkey Park and also spend 6/7 nights in Tokyo (split between the beginning and end of our trip).
We were looking at going to Kyoto, apparently it takes approx 6 hours travelling time from Kyoto to Hakuba. So we will give this a miss this time.
We are after some advice on where to go for 4 nights before we head to Hakuba? Maybe Nikko? Shirakawago Village?
Another piece of advice I would like is, public transport leaving Tokyo on the 2nd, or 3rd January as far as crowds go?
Kind Regards.

Hi. So I take it you are leaving Tokyo on the 2nd, right? Around that time most of the travel should be coming back in toward Tokyo.

Nikko is an overnight kind of place, maybe 2 nights if you are going to the lake as well. Personally I would spend 2 nights at Karuizawa and then maybe one at Besho Onsen (just off from Ueda also on the same shinkansen line) and maybe one at Matsumoto (continue with shinkansen on to Nagano, then a shortish train ride from there). That will leave you close-ish to Hakuba.

Bessho onsen is a nice onsen town with some decent sights, Matsumoto has a good castle. Karuizawa has some interesting sights and a great shopping street.

Nikko is one good choice. For just the central shrine area, you could do fine with a day trip if you get an early morning start. If you want to add Okunikko, then 2 days is better (but the sights are worth it).
From Tokyo it would take you over 5½ hours to get to Shirakawago. And you'd be done with it in just a few hours. Not worth it in my view. Although if you are going to Kyoto, you could add on Miyama.
https://www.japan-guide.com/e/e3985.html
You should definitely add at least a half day for Nara while there as well.
https://goo.gl/LfvWnL

Thanks so much for sharing your knowledge with me! It is so good to suggestions regarding places that I am not aware of.
Originally we were going to leave Tokyo on 4 January to avoid the crowds. But I am now hoping to leave on the 2nd or 3rd.
Would you suggest to see the snow monkeys on a day trip from Nagano?
Or should we stay at Shibu Onsen?
Thanks again,
Clare