Hi there,
It is likely worth it to get a 14 day JR Pass, as travel to Hiroshima, Kyoto and Tokyo will cover the major part of the pass but it also depends on what day trips you plan on making. For instance adding a trip to Himeji and Nikko would give you great savings compared to purchasing normal tickets. While trips to Nara and Kamakura don't add that much in terms of travel costs.
All the places I mentioned above already make for great day trips. My personal favorite is Nikko. When the temple complex in Nikko was built by Tokugawa Ieyasu. He tried to set himself up as a God after death, the result is amazing. There's also a lot beautiful nature around Nikko, great for hiking.
If you want to see a beautiful Japanese castle, then I would also suggest a trip from Kyoto to Hikone. The town is often passed by western tourists and the castle is one of the most beautiful in Japan.
I can give you more suggestions if you let me know what you are interested in.
Hope this helps,
Daniel