Japan Rail Pass (7-day) would
not be the most cost-effective solution.
JR-West Kansai-Hiroshima Area Pass (5-day)
sounds suitable for your western Japan trips.
JR regular tickets to get from Tōkyo | Shinagawa to Kyōto
: Around 14000 yen per adult.
JR-West Kansai-Hiroshima Area Pass (5-day)
: 15800 yen (when purchased through the official website)
Unlike Japan Rail Pass
: This pass can be used
to take faster Nozomi and Mizuho on the Shinkansen.
: This pass is not valid for the Shinkansen between Shin-Ōsaka and Kyōto (#).
Himeji Station is skipped by many Shinkansen trains,
and some trains which make a stop at Himeji
are Nozomi and Mizuho trains,
which JRP travelers cannot take.
You can visit Himeji and Kobe
on your way from Hiroshima to Kyoto.
(If you visit the both,
it sounds better to stay overnight somewhere along the route
before you head to Kyoto.)
Hiroshima --[Shinkansen]-- Himeji,
Himeji --[Special Rapid]-- Sannomiya (in Kobe),
Sannomiya --[Special Rapid] -- Kyōto.
- Japan Guide: JR Kansai Hiroshima Area Pass
https://www.japan-guide.com/e/e2361_kansai_hiroshima.html(#)
Tōkaidō Shinkansen
(Shin-Ōsaka -- Kyōto -- Nagoya -- Tōkyō)
is operated by JR-Central.
San'yō Shinkansen
(Hakata -- Hiroshima -- Okayama -- Himeji -- Shin-Ōsaka)
is operated by JR-West.
When you travel with this JR-West pass
between Shin-Ōsaka and Kyōto,
you go by the conventional [non-Shinkansen] line.
Special Rapid trains are available frequently
between Himeji and Kyōto.