Worth buying a jr pass?

Hi,
It comes close, but a 2 week JR Pass would pay off - even better if you take a few day trips and extend your itinerary a bit.
When you get to Japan, the renovations will have been completed for Himeji Castle (Japan's finest), after many years of work, and it would make a splendid side trip for you.
For Kyoto, be sure to take at least half a day and see Nara as well. When the Kyoto temples/shrines close around 5PM, you can easily zip over to Osaka and enjoy the night life there. Dotonbori is a must see place. And the views from the Umeda Sky Bldg and Abeno Harukas Bldg are spectacular.

https://www.youtube.com/watch?v=COJ_MeXbeow

https://www.youtube.com/watch?v=xb1wuyAGgyQ

https://www.youtube.com/watch?v=-AyUZmGbW8g

For Hiroshima, IMHO one day is enough to see Hiroshima City, and one day for Miyajima. You can use the extra day to explore nearby sites like Iwakuni, with its iconic bridge and mountaintop castle. It is also good for cherry blossoms:

https://www.youtube.com/watch?v=0COOZXi66mM

You can see it in a few hours. You can also spend some time in Okayama, which has one of Japan's most famous historical gardens, Korakuen, as well as a lovely and almost unknown garden, Handayama:

https://www.youtube.com/watch?v=5zAI3_N7NEM

https://www.youtube.com/watch?v=JGQ8o7k9GbA

Or if you prefer, there is the beautiful Kotohira in Kagawa, Shikoku. It's famous for its shrine and mountaintop view, but it is the climb up that is the real adventure:

https://www.youtube.com/watch?v=ley9rVIewoQ

Another choice is the little known city of Onomichi. It has a hillside temple tour you can take; but its real treasure is an almost unknown temple on one of its small islands - in fact it's been thought of as almost a Buddhist Disneyland:

https://www.youtube.com/watch?v=97Q5EjEOXI8

For the Tokyo area, some popular day trips are Nikko, Kamakura/Enoshima, and Hakone.

Take lots of memory cards and a good camera - you will probably be taking a ton of photos.