A 14 day JR Pass is ¥45,100, so lets take a look at your individual ticket costs to see if they'll be more than the price of a pass:
- Tokyo > Kyoto: ¥13020, (164mins, 513km)
- Kyoto > Hiroshima: ¥10590, (112mins, 380km)
- Hiroshima > Saijo: ¥570, (35mins, 31km)
- Saijo > Yanai: ¥1890, (133mins, 106km)
- Yanai > Miyajimaguchi: ¥950, (65mins, 52km)
- Miyajimaguchi > Saijo: ¥950, (64mins, 53km)
- Saijo > Hiroshima: ¥570, (37mins, 31km)
- Hiroshima > Tokyo: ¥17850, (292mins, 894km)
TOTAL: ¥46390 for 8 legs
As you can see the rail pass comes out at a saving of ¥1290 vs standalone tickets. In addition to this saving you also gain convenience and the flexibility to change your plans should you need to at any point during your trip.
Hope this helps!