We went in oct 2019. Loved it. Best trip ever. Business hotels were cheap and excellent value. Every hotel we stayed in (booked via booking.com) was 3-4* and all had literally everything- PJs, shampoo, umbrellas, sometimes free dinner?! So good. Service was excellent and everyone was tripping over themselves to help us.
Get the rail passes delivered to you in the uk before travelling. Look up where you can use them- it included some regional trains I think the one up to the 32k tori gates in kyoto for example and an airport train to one of the Tokyo airports (can't recall which)
Their equivalents of Oyster cards were easy and useful to use at nearly all vending machines across tokyo and kyoto as well as for buying food on the bullet trains. Random but handy. We found 7/11s everywhere were also useful for picking up lunch on the go.
In Tokyo the government metropolitan building was a great free viewpoint, we went at sunset. we loved the senso ji shrine and meiji jingu. Tsukiji fish market was a fun lunch trip. We wanted to do the tuna auction but it was soo early in the morning we were too tired. The crossing at shibuya is awesome- we went and got a hot chocolate from the Starbucks above just before bed and sat people watching in awe of this crazy city. TeamLab borderless we LOVED. Got there first thing and absolutely loved it. But look it up and see if it's your scene. If not, skip! We went to akihabara one afternoon and found lots of Mario kart games machines which we had fun reliving our childhoods with. I avoided the exotic animal cafes as there were issues with how well the animals were looked after.
We went into kyoto which was so different but absolutely worthwhile. Dinner in Gion and looking for geisha girls (look out for Chinese tourists who dress up as them though!), the gold leaf shrine (kinkaku-ji) was stunning and then afternoon trip up to fushimi inari taisha with the thousands of tori gates. It's much older with v few skyscrapers but there's a temple on every corner and we just LOVED it. There is an underground (I think) but it only runs in 2 directions so we took a lot of buses via google maps. We also did a tea ceremony and Mochi making - found the company via tripadvisor but found this super interesting and the staff were lovely. There's also the bamboo forest with monkeys but sadly we had a typhoon hit so never made it there! You need 3 nights at least I think in kyoto..
I think if I were doing 14 nights I'd probably look into a stay in Hakone where there are views of Mount fuji and a much slower pace of life. I've never been able to find the perfect hotel for us there, though so that's held us back a little.
We stayed for several nights on the South Island due to other reasons we were there. There wasn't much there and I wouldn't recommend it but a trip to Hiroshima might be educational. Not sure if I'd take DC as young as 9 though if I'm honest. It's pretty dark
Autumn is a great time to go. You might catch the autumn leaves which imo were absolutely beautiful. You can I think google a website that'll tell you their forecast in different parts of Japan so you'll know if you're likely to see them in their peak bloom!
Finally, the food is fantastic in Japan! I am severely allergic to wheat and everyone was SO helpful and accommodating I really ate so well and felt so safe. The people and their kindness really blew us away. Enjoy! It's the trip of a lifetime!