Hello Benjamin,
Knowing what you would like will ensure that you get the most of your time in Japan. Looking at your wishes, it is certainly possible with a bit of good planning.
The 7 JR Pass will offer amazing value here as well. Think about this, a normal return ticket Tokyo - Kyoto alone is almost the price of a 7 day JR Pass. Amazing savings can be had, with all the additional travel added in. Normal tickets Kyoto - Hiroshima alone cost 20,000+yen without the JR Pass.
As for onsen visits, there are a couple of options that come to mind.
1.) Kurama Onsen located in the north of Kyoto, this would be the one most easily incorporated in your itinerary. The area is also very nice to hike trough and Kibune Templem, the closeby temple, is wonderful too.
2.) Kinosaki Onsen The name somewhat gives it away - this is a town dedicated to onsen. Best visited with a overnighter at one of the local Ryokan, this is one of the best places to enjoy an Onsen in Japan.
3.) Arima Onsen About 90 minutes from Kyoto and closely located to Kobe, this is one of the most famous onsen in the Kansai Area. Also well worth a visit, a great bonus is that can be accesed by rope way which connects to Mount Rokka, from where a view of the entire Kansai Region can be seen. Very romantic when night falls.
Takayama is also fantastic (Japan has too many great places), however I feel it may feel like a rush job if this we would try to put it in besides Kyoto, Nara, Onsen visit, Hiroshima and a stopover for Fuji.
Coming to Fuji, would advise a visit to Hakone. This area can be visited with the Shinkansen and is directly on the route between Tokyo - Kyoto, so you could visit before going to Kyoto or when returning to Tokyo. More on Hakone can be found here.
Hope this helps,
Daniel
Hope this helps,
Daniel