I'm staying in Kyoto for five nights and am planning to travel to Osaka a few times and a day trip to Hiroshima.

I'm wondering whether to get the JR Kansai-Hiroshima pass (17,000JPY) which is only in ordinary class. Or buy green car tickets each way for 15,400JPY, and then a JR Kansai pass for four days (7000JPY for four days)

I would definitely get the JR Kansai-Hiroshima pass because of the Hiroshima trip. You would take JR rapid trains between Kyoto and Shin Osaka to transfer to/from the shinkansen to Hiroshima. Am pretty sure you can also use limited express trains to get to Shin Osaka and Osaka Stations. The ordinary cars on the shinkansen are comfortable and you can get free seat reservations with that pass. Green car is unnecessary. You can also use the pass on the JR lines in Osaka or in Kyoto if you want to go to Arashiyama. Pretty much a no-brainer.

OTOH, if I wanted to avoid the transfers each way to Hiroshima then I would consider just buying a ticket from Kyoto to Hiroshima with no transfer. JR West gives 5740 each way in ordinary car or 9400 in green car.

Thank you, that is very helpful. How can I get these discounted Shinkansen prices?

Sorry, I made a dumb mistake. I only gave surcharge amount yesterday. The cost would be 12,340 ordinary or 16,000 green car on a Nozomi. That includes the base fare and the surcharge.

Use the Timetable & Route Finder here:
Route Maps and Timetables | West Japan Railway Company
Be sure to set the departure time to something reasonable. The default is current Japan Time (23:30 at the moment).

That 7000-yen pass sounds like overkill. It would be difficult to spend that much on regional travel in four days. You need to work that out based on how much you would actually use it and on how many days. Or maybe you don't know or don't care about saving money and just want a sledgehammer solution. That is, maybe the 7000-yen (50 bucks) pass price is low enough so that if you got to use only one-third or half of its value then that would be within your pain threshold.

Not clear on your length of stay in Kyoto or where you are coming from or going to. Traveling to/from Kansai Airport would get more value out of either pass.

JR Kansai Area Pass
JR Kansai Hiroshima Area Pass

That is true, I'm staying at Kyoto Station (Doubletree Hilton) for five nights and then Swissotel Namba for the last (sixth) night. Flying into ITM and out of KIX so would be taking the train. Maybe the pass would be worth it taking Haruka between Kyoto and Osaka, but perhaps just best to stick to point to point tickets.

If you are going to Hiroshima the Kansai Hiroshima pass will save you money. You just have to work out which 5 days you want the pass to cover.

Consecutive 5 days. Just pointing this out since some regional JR passes used to allow X of Y day like 3 JR travel days in a 10 day period.

Passes that can be validated for use on non-consecutive days are a dying breed. Too bad, as they were really useful. The only pass for non-consecutive days that I can find today is the Kansai Railway Pass:
https://www.japan-guide.com/e/e2357_005.html

Are you aware of others?

Frankly, all rail passes seem to be getting less attractive. I mostly find myself telling people not to bother.

Ok, a 7-day trip. You will take the airport limo bus to Kyoto Station and then walk 3 min to hotel. No need for the pass that day and maybe not the next, so your inter-city travel could be on the last five days. Using a pass might save some money. There is an added cost - the transfers at Shin Osaka to/from Hiroshima. That would be worth $20 to me to avoid plus a bit more for the comfort of the shinkansen vs maybe standing on the JR rapid train. But YMMV, of course. You won't be carrying luggage on that day trip making the transfers a bit easier.

Please don't forget to include Miyajima in your day trip to Hiroshima, I'd go there first. It's quite feasible to do both in a long day trip from Kyoto. Even the ferry to Miyajima is included with the JR pass (although it's not pricey anyway).

I am also planning a day trip to Nagoya too, but none of Kansai region passes seem to be valid there. Thank you for the ferry suggestion, I will also visit Miyajima!

Nagoya is not in the Kansai region and, more pertinently for this discussion, the JR railway in Nagoya is JR Tokai - not JR West, so it isn't included in passes issued by that company. The area covered by the Kintetsu rail pass stretches from Osaka to Nagoya - but is only valid on Kintetsu railways. I think it's unlikely to be a helpful option for you.

Only pass that covers places in Kansai as well as Nagoya is the mentioned Kintetsu 5 day pass.
https://www.kintetsu.co.jp/foreign/e.../krp_5day.html
You’d still need to book and pay the supplement for premium trains on that network though.

I’ve been arranging a month long tour for my mother where she never stayed longer than three days anywhere, and couldn’t find a suitable rail pass for her. With one exception: the Hokuriku Area pass (a 4 day pass for 7,000yen). Happily, it forced a visit to the Kurobe Gorge railway.

And that’s the reality of rail passes; to save money with passes you need to arrange an itinerary to suit the pass not get a pass to suit an itinerary.

That is true, I think I might stick with point to point tickets.

As I stated before, if you are going to Hiroshima the Kansai Hiroshima pass will definitely save you money. There are no downsides to it. It will also save you money if you go to Miyajima, and on JR trains in and between Kyoto and Osaka and between either of those places and Nara. The only thing you can’t use it for is the Shinkansen between Kyoto and shinOsaka but you can use the Thunderbird instead, which is all reserved seats.