You can probably get by on two passes and an IC card. It's possible, if you want to go to Kanazawa, which is a very beautiful city, to do this with only one Pass and an IC card. I'm going to suggest that you get two passes.
The first is the Takayama-Hokuriju Tourist Pass, which will take you from Nagoya to Takayama, and to Shirakawa-go by bus. After your half day at Shrakawa-go, I would advise you to go to Kanazawa, but you could backtrack to Takayama, if you wish.
http://www.japan-guide.com/e/e2361_takayama_hokuriku.htmlThis pass will take you all the way to Osaka, if you want, but you could backtrack to Nagoya.
You will still need to get from Nahoya Airport to Nagoya station, and at the end of your trip, you will need to get to Kansai Airport. My sugestion is the Wide version of the Kintetsu Rail pass. It has two airport transfer tickets that will work at either Nagoya's airport or Kansai Airport, it also includes a five day pass around Osaka, Nara, and Kyoto.
http://www.japan-guide.com/e/e2357_006.htmlYou are staying at Shinsaibashi, which is close to Namba Station. The Kintetsu pass should work out for you.
Going to Kobe and Himeji could be done with an IC card. There are private trains from one of the Namba stations to those locations. The Hanshin private line will take you from Osaka-Namba Station to KosokuKobe Station for 540 yen, and it will also take you to SanyoHimeji Station for 1370 yen.
Another option is to just pay for an airport shuttle to Nagoya, use the Takayama-Hokuriju Tourist pass from there, and add a JR West pass, a JR Kansai Wide area pass after that.
http://www.japan-guide.com/e/e2361_03.htmlhttp://www.japan-guide.com/e/e2361_08.htmlI think these are better options over the seven day JR Pass.