If you can see what you want in the Tokyo area first, then go down to Hiroshima/Miyajima and return to the Kansai area within a week, then a 7 day pass would pay off. You could save quite a lot with that.
You could also take a day trip to Nikko north of Tokyo within the week to add to your savings, and a day trip to Himeji (with Japan's finest castle) would enhance your value further. You should also add Nara to your itinerary for at least half a day.
Nara is often neglected by some tourists, which is a shame. Missing the Todaiji in Nara is like going to India and skipping the Taj Mahal. Nara Park has a lot of great places. A few other great places missed out even by those who go to Nara though are the Isuien
https://www.youtube.com/watch?v=kk-7IoLELioand Yoshikien Gardens. They are gorgeous and not crowded at all.
In addition, there are other numerous great places you can visit in the area. Okayama is not far and it is famous for its castle, plus Korakuen
https://www.youtube.com/watch?v=5zAI3_N7NEM which is one of Japan's Top 3, and also the Handayama Garden
https://www.youtube.com/watch?v=JGQ8o7k9GbAIf you'd like to get off the beaten trail for a while, the half day hike up to Konpirasan in Kotohira, Kagawa
https://www.youtube.com/watch?v=ley9rVIewoQis stunning. Going to Takamatsu is also nice - it has one of Japan's finest gardens also, called Ritsurin.
https://www.youtube.com/watch?v=afx-Ju52FiY And aside from Hiroshima/Miyajima, Onomichi with its temple tour and Kosanji Temple
https://www.youtube.com/watch?v=97Q5EjEOXI8is spectacular. Just beyond Miyajima also lies Iwakuni
https://www.youtube.com/watch?v=0COOZXi66mM with its historical bridge and castle on top of the mountain.
And if you really want your socks blown off, visit the 300 million year old limestone cave in Yamaguchi, called Akiyoshido:
https://www.youtube.com/watch?v=DqIKC9S8TFQAll in all, a lot more to explore and enjoy.