Fukuoka to Toyko Itinerary 7-9 days

My daughter (17) will be taking language classes in Fukuoka and her brother (mid 20's) will be meeting her at the end of her program to explore more of the country together. We were thinking they could spend a day in Fukuoka together before working their way to Tokyo. Places they'd like to visit include: Hiroshima, Kyoto, Osaka, and Ghibli Park. They'd like to spend 3 days minimum in Tokyo before flying home. An alternate idea would be to have our daughter fly from Fukuoka to Tokyo to begin and end their trip there. We are trying to decide if they should buy train passes individually or do a 7 day rail pass, and whether they need individual passes for each location. Our daughter will likely have a Fukuoka City Pass during her stay and we read about a Fukuoka region day pass for tourists while our son is there for a day. We plan to look for inexpensive lodging or Airbnb type rentals along their trip. We've also considered trying to find a travel agent who is an expert and can guide us, but am starting here instead. Thank you!

How many days your daughter stays in fukuo ka?how many days your son stays in japan?

Pl use this to calculate yr fares, schedule
https://world.jorudan.co.jp/mln/en/?c=10&sub_lang=nosub

Then decide if a JR 7 day national pass is viable- most likely not at a glance.
An IC card will be more useful.

Booking 21 days ahead on this site, if travelling long distances may be an option.

https://smart-ex.jp/en/beginner/

You can find lots of information on Japan guide site to aid your planning.

A 7 day nation wide pass would just pay off depending on your side trips. Trams in Hiroshima, subways in Kyoto/Osaka cannot be used.

But some of your party cannot get a pass anyway. So might be worth not bothering.

Daughter will be in Fukuoka for 28 days and then my son will arrive and they would like 7-9 days together exploring.

Why is one of them not able to get a pass? Is it that 17 is too young? Thank you. Also, any suggestions for itinerary and budget stays is appreciated!

Well your original post suggested she was a student. So long term resident, hence not being able to get a JR pass. Just a assumption.

But then later you say she is here for 28 days. So now assuming she is a temp visitor, which can purchase a JR pass.

As your daughter will stay in Fukuoka for 28 days,so i suggest to buy fukuoka subway 30 day pass=12570 yen,known as chika pass

She will oriented with her city,so she must buy 1 day nishitetsu bus pass=1000 yen, valid whole of fukuoka city

As a residence of japan,we cant buy JR pass
Or JR kyushu pass,but your daughter can buy
7 day whole kyushu pass=20000 yen