Worth to buy JR Pass

I have below itinerary for 2 person and thinking of buying a JR pass, but not sure if it is worth and if so, when to activate the Pass

Day 1. Osaka KIX arrival, to Kyoto
Day 2. whole day visit Kyoto
Day 3. Whole day visit Osaka from Kyoto
Day 4. Day trip to Nara from Kyoto
Day 5. Day trip to Takayama from Kyoto
Day 6. Kyoto - Tokyo
Day 7. Day trip to Nikko from Tokyo
Day 8. Day trip to Hakone from Tokyo
Day 9. Flight home from Narita apt.

I will leave for Japan soon next week (in sakura peak season), so cannot book room now in Nikko andn Hakone. I have my friend's apartment to Koyto to stay, so want to be there a much as possilbe.

Thanks for your kind advice by return, if above itinerar is possible and worth with JR Pass.