10 Days in Japan

Hello, We will be in Japan this Spring for the first time (small family). I've done a lot of research and put together the following itinerary. I'd love any thoughts in general. Most importantly, I am wondering about Hakone. The ryokan are very expensive. Is it a definite must see? How crowded is it? We are active and generally off the beaten trackers. Would it be worthwhile to only stay one night to decrease the cost splurge potential? It would help budget wise, yet I think we might feel rushed. THANK YOU!

4 nights (evening arrival + 3 full days) in Tokyo (with day trip to Nikko)
1 night Kanazawa (new 2.5 hr JR connection will be running)
1 night Shirakawa-go (maybe visit Takayama via bus)
3 nights Kyoto (with day trip to Nara)
2 nights Hakone (or 1 night Hakone/ 1 night Tokyo)

I haven't been to Hakone , but from words from a friend who go to Japan often, Hakone is very big and 2 nights are mostly recommended. However, bad weather might also ruin your stay there depending what you are going there for (was bad weather when my friend went there for 2 nights... )

For Ryokan, it is the best example of you pay for what you get, the better the room, the better the meal, the more expensive they get, what is your budget per person?

Other than that I feel your itinerary is reasonably spaced out, except the day after Shirakawa-go, if you visit Takayama you probably will be required to take train via Nagoya to Kyoto which might be a little longer than Thunderbird from Kanazawa (on top of my head)

Some people will complain that why there is no Osaka trip though (not that I care, not much fan of Osaka at the moment) but you probably unable to squeeze another city in anyway.

Agree with the person above. With that many days in Tokyo, you can skip Osaka.
If you are the "Off the beaten track" kind of person, then you might want to cycle around and away form Hakone.
Better yet is to go west/south of Fuji. It is less popular as it is not as developed but there are still onsen and ryokan available. Maybe get yourself some unagi? Or stay in Yamanashi small towns. (Try the town with the least Japanese inhabitants)

Thank you both! Yes we want to take the quicker Thunderbird from Kanazawa so I think Takayama may be out unless we visit it as a day trip from Shirakawa-go the day before leaving for Kyoto. Might be more relaxing to stay put in Shirakawa-go and hike or something though.
We have 2 adults and 1 child and I was hoping to keep Ryokan budget to 8000 yen a night per person max. Seems difficult with Hakone options. Thank you for the advice on other Fuji areas. I am checking out Yamamashi now.

When is your trip roughly? And how old is the child? I could help you have a look at what is available if I can get these details.

Thank you! April and age 10.

Not in order just searching based on price and number of people:
http://www.fujiyahotel.jp/
http://www.hotespa.net/hotels/mizunoto/
http://www.hotespa.net/hotels/setsugetsuka/
http://www010.upp.so-net.ne.jp/rokkaso/
http://www.itari-tei.com/

Not all are Ryokan type, some are Onsen hotel, and most do not have April schedule up yet.

And the search is based on the whole Hakone region so I have no idea where is the hotel/ryokan that I have listed...

Thank you!!! I did not think Fujiya was on budget. I will double check that one for sure as well as others.