My experience is fairly Kansai centric, but here are some thoughts.
It looks to me like you have a lot of time in Tokyo. I don't know the city well enough to know if you need that amount of time.
There is a small ancient city called Nikko. It is an easy day trip from Tokyo. We enjoyed it. Take a look, it might be interesting to you.
Agree that two nights in Kanazawa makes a lot of sense.
Kyoto is wonderful. It is a bustling city in between all the tourist sights. Take a look at the Philosopher's Path. From memory, it takes you to some very nice, out of the way sights. Two of our favorite day trips are easy from Kyoto.
Nara Park is in the city of Nara. I expect you can get a walking map online or at the train station. Walking the loop around the whole park will help you feel like you are in old Japan. Feed the deer!
Himeji. The Himeji Castle is stunning and much better than some of the others. In Himeji, there is also a very rustic temple on Showa Mountain. Parts of the Last Samurai were filmed there.
My wife LOVES pottery. If this is a strong interest for you, look up Japan's ancient pottery towns and see if any of them make sense.
You might want to take a flight to another part of Japan with your open days. Perhaps either Nagasaki or Sapporo.
This sounds like a great trip.
Enjoy