Brisbane: I believe there is a koala sanctuary outside of Brisbane. The south bank area offers a lot We also did a day trip to O'Reilly's in the Lamington National Park. Had lorikeets eating out of my hand and sitting on my head. Our children (aged 10 and 13 at the time), were sort of happy to hang out in the apartment we had rented. They did like the river ferry system which is quite efficient.
Melbourne: The Old Melbourne Gaol peaked their interested, but might not be appropriate or interesting for your 10 year old. We were there in winter, so our interests were different.
Sydney: Husband and kids stayed in the Rocks area. Went to one of the beaches. I caught up with them just in time to fly to Cairns.
I would do some research as to what is in each city. We've held koalas, daughter held a wombat. We drove a campervan from Cairns to Brisbane.
Suggest purchasing a Lonely Planet or other guide. Or checking some out of your local library.
Australia is wonderful! We are planning on going back in 2020.