It really depends:
Japan Rail Pass pricing
7 days 29110 Yen
14 days 46390 Yen
Shin-Kobe to Tokyo round trip would already cost 29360 Yen
If you could fit everything in 7 days then the 7 days Japan Rail Pass would be worth it, however you will not be able to take the fastest Shinkansen.
From Kobe
Osaka not going to cost to much
Only Nara, and Kyoto would only be about 2500 Yen round trip each.
I would use Rail Pass for Shiga and maybe other places like Himeji, Hiroshima, and Tokyo.
Maybe something like this
Japan Rail Pass
D1 ShinKobe or Sannomiya Station Shiga Day trip
D2 ShinKobe to Himeji to Hiroshima, having day trip to Himeji and on to Hiroshima
D3 Hiroshima and Miyajima Day
D4 Hiroshima to Tokyo, Morning train arriving in Afternoon
D5 Tokyo
D6 Tokyo
D7 Tokyo to ShinKobe Evening Train
Regular cost
Not sure which part of Shiga your going to but lets just say Hikone, Sannomiya to Hikone 4540 Yen round trip
Shin-Kobe to Himeji to Hiroshima 11510 Yen
Hiroshima to Tokyo 18560 Yen
Tokyo to ShinKobe 14680 yen
At least 49290 yen cost for this which is great savings for you using the Japan Rail Pass BUT your girlfriend would have to pay the regular prices as you can only use Japan Rail Pass if you are visitor tourist visa.
Just an example of how to use the Japan Rail Pass. You should price out the itinerary here
http://www.hyperdia.com/en/cgi/en/search.html?dep_node=TOKYO&arv_node=...Hope this helps!!
Have fun!!