We (2x adults and 2 x teens) went 8-25 October last year - it was much hotter than we had thought it would be - no need for a jacket at all, just umbrellas (from Family Mart) and hoodies (from Gu).
We did 6 nights Tokyo, 3 nights Hiroshima, 5 nights Osaka and last night in Tokyo.
We arrived at Narita after a long flight and were a bit bewildered by the ways to get into town. Someone offered to help us - but it turned out that that person was a taxi driver (we were very tired and a bit stressed by it all) - so we ended up getting a (maybe dodgy) taxi from narita to our Tokyo apartment - but we were driven straight to the door and we didn’t need to humpff luggage about Tokyo, so I think it worked out OK (it was about £100 for the 4 of us).
We stayed between Ueno and asakusa in Tokyo - it was quiet, felt really safe and walkable to tube/train stations or a 10 min walk to Ueno station (which seemed huge when we went to get the girls Suica cards (no iPhones) but you quickly get used to it!).
i can’t remember the area we stayed in in Hiroshima but it was a Nest Hotel close to a tram line. It was handy but a bit out the way, so quite quiet - but the rooms came with hotel pyjamas that the children liked.
We stayed in the OMO 7 hotel in Osaka - it was a bit out the way too - but right next to the train/tube. The hotel had lovely gardens - even in the rain. There was a shopping mall about 10 mins walk away - had all the usual shops but not as busy as the centre of Tokyo. We did day trips to Kyoto and Nara from Osaka rather than stay in Kyoto just to reduce moving all our stuff (though we didn’t get to Kobe unfortunately).
We spent our last night at a hotel at the airport (narita) which was fine (had a pool!) but in hindsight I wish we had just flown home from Osaka rather than traipsing back to Tokyo for a night to catch a flight home (we flew over Osaka on the way back home).
We only used the Shinkansen once - between Hiroshima and Osaka - mostly due to cost tbh. Internal flights are very efficient and cheaper than Shinkansen tickets but on balance - Shinkansen is probably quicker and less fussy but the differences in prices for us meant the teens could spend even more money on skincare and anime models….
You will have a great time regardless of the weather - don’t over plan - it’s a holiday!