Tokyo - Kyoto = ¥13,060
Kyoto - Hiroshima = ¥11,090
Hiroshima - Tokyo = ¥18,560
Total = ¥42,710
7 day JR Pass = ¥29,110
QED

Although I would always argue for more time in Kyoto (and less in Tokyo), that won't work for a 7 day JR Pass; you need the Pass to start on day 6 (after 5 nights in Tokyo) when you go to Kyoto and still be valid on day 12 when you travel back to Tokyo (presumably to fly home).

The only downside to a JR Pass is that you can't use the Nozomi Shinkansen, the fastest (because they make the fewest stops) and most frequent trains. However, that's usually not an issue. Most trains from Kyoto to Hiroshima require a change of train at Shin-Osaka; however, there are two Hikari Shinkansens at 7.20 am and 8.00 am that do not require a change, so best to use those if you can.

Get a Suica card as soon as you arrive to use in Tokyo and for the subway/buses/local trains/vending machines/convenience stores everywhere. It makes life much, much easier. If you have an iPhone 8/X/XS, you can add a virtual Suica card to Apple Wallet and then use Apple Pay to top it up. Regular Suica cards need to be topped up -- cash only -- at a ticket machine.

While it depends on your interests, I'd say that for most first visitors to Japan, your allocation of time makes sense. For my interests, I'd shift a night fromTokyo to Kyoto -- but that's just me.

If you haven't already done so, do spend lots of time with japan-guide.com.

Enjoy!

I'd put 4 nights in Tokyo and 5 nights in Kyoto. Kyoto is spread out. Plus, from Kyoto one can zip to Osaka, if one chooses, as it's close by by train from Kyoto train station. I zipped there for a half day and it's only 560 yen, one way, on the train and half an hour. Also Kobe is nearby if you want to add another thing to do while in the Kyoto area. I do 9 nights in Kyoto and plan to zip to Kobe for a half day and then back to Kyoto on the summer 2019 trip. One of the workers at my hotel in Kyoto commutes from Kobe to Kyoto daily and suggested that I just go for a day trip. There's lots to do in the Kyoto region.

Happy Travels!

After you get back to Tokyo what will you do next?

going home

In that case, let me ask: Have you already booked your flights? if not, explore your options for flying into Tokyo and out of Osaka or vice versa.

If that means that you are flying home from Narita Airport then you can just fly from Hiroshima to Narita Airport. A one-way flight could cost US $98 on ANA or maybe less with another carrier.