Deciding on a rail pass

Hi,
Yes a 14 day pass will pay off for your plans. Although please know with a good connection it'll take you about 5 hours to get from Nozowa Onsen to Kyoto. From Tokyo to Nozowa Onsen it can take 2-3 hours - check Hyperdia for schedules.
For Hiroshima, be sure to spend at least ¾ of a day to see Miyajima. For the Kansai area, be sure not to miss Nara and Himeji. Since you are already seeing Tokyo, you can largely skip Osaka during the day. After the temples of Kyoto close down around 5PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are wonderful. You also might consider spending a night at Koyasan. The JR Pass will save you a lot getting from city to city, but it's not so useful for within the cities. In Tokyo and Osaka you can use them for a couple of loop lines, otherwise you'll need to pay for other buses or subways.
For day trips in the Tokyo area, take a few good day trips to Nikko, Kamakura/Enoshima, Hakone or the Fuji 5 Lakes Area.

Thanks for the reply Toraneko - really appreciate the suggestions and can't wait to add some of these places to our itinerary!