Osaka - nara- Himeji - Tokyo

Hi,
If you travel to all the places you mention (particularly Himeji & Hiroshima) above and go to Tokyo within a week, then yes a 7 day pass will save you a tidy amount of money. For Hiroshima don't miss Miyajima - you can use the pass to ride the JR ferry. A bit beyond is another great sight if you have time, at Iwakuni with its iconic historical bridge and mountaintop castle.
For Tokyo if you want to travel all over, you might look at a Kanto Area Pass - you can go to Kamakura, NIkko, Karuizawa, Kusatsu, Izu, and many other popular places. If not, there are other passes for Hakone, the Fuji 5 Lakes, Kamakura/Enoshima etc by Odakyu.

Best of luck.