Itinerary check and JR pass optimization

Hi!

Im going to Japan for the first time in September and will be staying two weeks. I have the first 6 days figured out already but don't know how to optimize the final 8 so I hope you can help me. The preliminary itinerary looks like this:

Day 1: Arrive in Tokyo, Narita airport
Day 2: Tokyo
Day 3: Tokyo
Day 4: Tokyo OR day trip to either Kamakura or Nikko and back to Tokyo
Day 5: Hakone
Day 6: Hakone
Day 7: Takayama
Day 8: Kanazawa
Day 9: Kyoto
Day 10: Day trip to Nara and back to Kyoto
Day 11: Kyoto
Day 12: Kyoto
Day 13: Osaka
Day 14: Fly home from Osaka Kansai airport

My first question is: Im thinking about buying and activating a 7 day JR Pass on Day 5, do you think this is a good idea given the fact that Im flying back from Osaka?. The other questions concern the visit to Kanazawa and Takayama --> are there any possible ways of getting there only using the JR pass? If not, when looking at hyperdia i see that parts of the journey looks like it is covered by the pass but the price is not broken down, is it possible to book a ticket and only pay extra for the part of the route not covered by the JR pass?
Do you have any ideas on how I can improve the itinerary and be able to visit these places in a more time efficient way?

Thank you for your help

Best regards

Jasmin