First time in Japan - 12 days

Hi,

I have planned the following itinerary for our 12 days in Japan in mid-November for 2 people. I have arranged the travel dates such that I we can use only a 7 day JR pass. Would you be able to provide a breakdown of the travel costs for each of our major travel days so I can determine whether it would be worthwhile to have a little more flexibility in our travel schedule (perhaps an extra day in Hiroshima at the expense of a day in Tokyo) and go for the 14 day pass instead? Also, would a JR pass cover travel in and around Tokyo?

Day 0: Flight arrival at 10:30 pm at Haneda. Sleep Tokyo.
Day 1: Tokyo. Sleep Tokyo.
Day 2: Tokyo. Sleep Tokyo.
Day 3: Tokyo. Sleep Tokyo.
Day 4:: Early train to Nikko. day in Nikko. Back to Tokyo. – START JR PASS
Day 5: Early train to Kyoto. Afternoon and evening in Kyoto. Sleep Kyoto.
Day 6: Kyoto. Sleep Kyoto.
Day 7: Day trip from Kyoto to Nara, Sleep Kyoto.
Day 9: Day trip from Kyoto to Osaka/Kobe. Sleep Kyoto.
Day 10: Early train to Hiroshima. Sleep Hiroshima
Day 11: Hiroshima. Back to Tokyo at night. - END JR PASS
Day 12: Tokyo. Back to Haneda at night

My partner is really interested in visiting the onsen hot springs. Is there anywhere in my itinerary that would be particularly good for that or should we be making a special trip somewhere else in order to experience a great onsen?

Thank you so much!!