Between 2019 and lock-down, I had 3 trips to Australia combining business and pleasure. I flew in and out and between various cities including Canberra, Brisbane, Cairns, Sydney and Melbourne. Connections were easy and multiple in my experience then and not unreasonably priced as I recall. I used Uber frequently, but I would check with TripAdvisor if that situation is still as convenient - it has changed somewhat in my US experience post-Covid, perhaps in Australia also.
If you are looking at Cairns, also look into Port Douglas. I stayed in both locations and took day trips to the Daintree rainforest from Port Douglas, Hartley's Crocodiles (which sounds terribly touristy but was a highlight), and a Great Barrier Reef snorkeling trip. From Cairns, I took another GBR trip, Kuranda, Atherton Tablelands. I was solo and didn't want to rent a car. When I traveled there were many day trips or shuttles to these areas. Cairns Botanic Garden and aquarium are good if you have time.
Re the GBR - I have been scuba and snorkeling since the 1980's. I have to say that the GBR was a bit disappointing - sadly, it is bleaching. The tour companies won't tell you this, so be sure to pick a tour company whose schedule and activities are of general interest and maybe one with several different sites. There are many companies, I think most are fine. Do expect that you might get sea sick, even if not normally subject to this. I had Bonine and was fine, but many others were not - a lot of sickness. I brought that from the US at my MD's suggestion. It is over the counter, but not sold in Australia. (although I'm sure Aussies have other seasick meds)
I preferred Melbourne to Sydney. Others are the reverse.
I enjoyed the government buildings, botanic garden, and museums in Canberra, but that may be a specific interest. Without knowing your particular interests, It is hard to suggest activities or areas of the countries. Could you indicate the types of activities or sites or interests you have?
I've seen a number of the animal zoos and shelters if you like that sort of thing. I can maybe give feedback on some in you find any of possible interest.
Caveat with all of this - situations, especially transport, may be different post-Covid. I found TripAdvisor to be the best source for current info and ideas of what I might most enjoy for the areas I was able to visit. I agree, the guidebooks can quickly be overwhelming.