Hi,
Given the length of your trip and the time you'd like to spend in each place, your itinerary is quite difficult in that any of the full JR Passes simply would not be economical.
So in your case you might explore several regional rail passes, as well as some air passes and specials to try and save money.
For the first part of your trip, you might look into a JR Kansai Hiroshima Area Pass:
http://www.japan-guide.com/e/e2361_kansai_hiroshima.html
With this pass, you can use the fastest bullet train, the Nozomi, to go see Hiroshima/Miyajima. It's also easy to go see Himeji, which is Japan's finest surviving castle. If you like, you could go a bit more and see Iwakuni as well, with its iconic bridge and mountaintop castle:
https://www.youtube.com/watch?v=0COOZXi66mM
There are some regional passes for the Kansai area as well - they may or may not suit you:
http://www.japan-guide.com/e/e2357_005.html
http://www.japan-guide.com/e/e2361_03.html
http://www.japan-guide.com/e/e2361_08.html
I noticed you didn't mention visiting Nara - which would be a tragedy if you missed it.
For the next part of your trip, there is a special pass to go see Takayama:
http://www.japan-guide.com/e/e2361_takayama_hokuriku.html
It also covers Kanazawa, which is well worth a visit.
To see Nikko, you might look at the Tobu Nikko Free Pass:
http://www.japan-guide.com/e/e2358_002.html
To fly to Hokkaido, there are some good air passes you can use - which one may depend a lot on what your international carrier is:
http://www.jal.co.jp/yokosojapan/
For Hokkaido, this is where it gets sticky. There are 2 Hokkaido Rail Passes you should consider:
http://www.japan-guide.com/e/e2361_01.html
http://www.japan-guide.com/e/e2357_001.html
However, especially in eastern Hokkaido getting around by train and bus is slow and inconvenient. Many people opt to drive, and one of the better places to look for info is on:
http://northern-road.jp/navi/eng/index.htm
There is an enormous amount of freedom in driving in the countryside, and many of Hokkaido's best places really need a car or motorcycle. Make sure you get the International Driving Permit (IDP) before arriving in Japan though. Two popular and cheaper places to get the car are at:
http://www2.tocoo.jp/en/index?
One of the biggest problems with your plan of driving though is the fact that there are stiff drop off charges for renting a car in Memanbetsu and dropping it off in Sapporo - the longer the distance, the heavier the charge.