Actually - there is another way you could space your trip that would let you maximise your flexibility with a 14 day rail pass if you don't mind rearranging your plans a little.
If you can move your Hiroshima visit earlier and ensure you will be back in Kyoto by the 7th of Jan, you make a similar saving as my first answer if you buy a 14 day rail pass running from the 24th -> 7th.
Your trip would look something like:
22/12 - Arrive from Melbourne into Narita. Train into tokyo (tickets at ¥3000)
23/12 - Tokyo (metro ¥500)
24/12 - train to nagano (first day of 14 day rail pass)
27/12 - train back to tokyo (Rail Pass)
3/01 - train to hiroshima (Rail Pass)
5/01 - train to kyoto (Rail Pass)
6/01 - maybe nara? (Rail Pass)
7/01 - last day of rail pass (Rail Pass)
9/01 - train to osaka. (¥500)
Bringing the total train travel costs to something around ¥49,000 with lots more flexibility to do day trips. This is compared to separates which would be around ¥55,000, with no flexibility.
Day trips like visits to Miyajima (from Hiroshima) and Nara (from Kyoto) will further increase the savings you'll make.
Phew! Hope this helps and is not confusing!