@SingaporeSlinky we stayed in Osaka and travelled to Kyoto and Nara from there. We found transport was fairly straightforward (but couldn't quite work out Osaka station, the shame!) so I am sure you'll be fine with staying in Kyoto and travelling around the region from there. It was worth it for us as it meant we could unpack properly and not move again for a few days, but it was just the two of us and adult DS so we weren't towing small people with us who might get bored sitting on a train.
We were away for 5 weeks and had 40L/10kg rucksacks so we travelled light and had laundry facilities in most places which was great. With hindsight I wish we had the same stuff in a bigger bag to allow for more souvenir space. I think we did much of our booking with Booking.com as you can filter for 'Washing Machine' as a room(?) facilty, so I can recommend them if you need to filter the laundry options. We also usually just book somewhere reasonably central and close to a tube station.
We enjoyed Osaka although Dotonburi blew DH's mind - it was far too busy for him but I loved the energy. One or two streets back it was much quieter so easily avoidable. By chance we went to a Buffaloes baseball game which was quite different from our experiences in US, although lots of food and beer were consumed there too! Osaka castle has been modernised inside so we didnt go in, but the footprint of the whole castle and grounds were impressive although busy. We had already been to Himeji Castle, which I recommend, as we had stopped in on our way from Tokyo to Hiroshima, we just left our bags in one of the many lockers in the station and walked to the castle.
Hiroshima is good, it is harrowing but I felt the messaging is "let's not do it again". There were lots of school groups around the park so it is presented in an acceptable was for teens I think. I wouldn't want to have missed it.
We just carried our luggage with us on the trains, as I say they are reasonably compact and fitted in the overhead shelf with no problem.
@Holidayqueen1 I hope i haven't derailed your thread with the info for SingaporeSlinky.
I think the costs for SK are siilar to Japan but its tricky to tell as most of Japan DH and I were alone but in SK we also had adult DS (who lives in Seoul) with us for some of the time too! I think he takes us to his favourite (and expensive) places!! We enjoy eating breakfast and lunch from the ubiquitous convenience stores, exploring all the mystery things to eat, if youre happy to this it should help with costings.
On our latest trip we left Seoul at the end of September and it was T-shirt to jumper weather, but Busan was pretty wet in mid September (we may have been unlucky). Their weather is fairly predictable and summer can be hot and humid. Our spring trip April to May was again t-shirt to jumper weather.
I think our favourite place was Seoraksan Nation Park, but have been mostly in Seoul with some trips to Jeju, Busan, and some other places. We've travelled on buses (opting for the mid range) and trains. On our first visit the trains were tricky to buy tickets online I think because we didnt have a Korean phone number or local bank or something, but on our second visit we travelled by train and booked in advance so i think the problem we had first time must have gone away somehow.... Buses were roomy and the service stations interesting. The train was also on time, clean and fast.
For both Japan and Korea (and elsewhere) I used Rome2Rio to find routes by public transport, highly recommended for the planning stages.
Do ask if you have more questions - love planning holidays!