In Australia, nearly every port has a wildlife preserve and a museum. You should probably pick out one of each and take a look but unless you have a special interest in either you may see a lot of similarity from port to port. Ports will often have an attraction that emphasizes indigenous culture. Again, depending on your interests, one may be sufficient. Sydney and Brisbane are fascinating cities which can be easily explored by foot and public transit which includes water transport.
In Sydney, we will dock at White Bay, the newest terminal, rather than Circular Quay or near Darling Harbour. This means we will pass beneath the Harbour Bridge. It appears to be about 3 km to the Balmain East Ferry Terminal but there may be shuttles or bus service but reports have not indicated transportation is easily accessible. Ferries shuttle between Balmain East and numerous other destinations. One can easily spend a day in the city and see the Opera House, Botanical Gardens, Government House, The Rocks, Dawes Point, the South tower of the Sydney Harbour Bridge, and a number of interesting restaurants in the Darling Harbour area. On the other hand, you can take a tour (ship or private-I would have to refresh my knowledge on operators) out to Katoomba and the Blue Mountains. It is a beautiful trip and the tram ride, canyon and nearby points of interest are well worth seeing if you have time. It can be very crowded and timing uncertain if you take a private tour or attempt to do a self-tour. Sydney has some nice beaches but unless you are a beach addict pass on this one. There are many other beaches. Remember, we spent two weeks in the Sydney area and we could easily do it again and repeat very little.
In Brisbane, the ship will berth at the mouth of the Brisbane River which is about 15 km from the city. In the city the river is used as a highway travelled by small boats called CityCats. While there is much to see in Brisbane you might consider a tour that covers a lot of ground. A trip down the coast could give you good look at the the coast and visit the famous Gold Coast and Surfers Paradise. We spent a few days in Brisbane but traveled the entire coast south of Brisbane.
Port Douglas is small and very tropical. This may be the only opportunity to visit the Great Barrier Reef. Even if you do not wish to snorkel or scuba dive you can get a look at the reef in a submersible. The boat ride to and from the reef can be a stomach churner. The Daintree is spectacular as is Kuranda. I think the Kuranda is unique to this port whereas I believe Darwin offers rainforest experiences.
Near Melbourne is one of the most amazing wildlife exhibits, the Healsville Sanctuary. Having visited several wildlife preserves while in Australia I would choose Healsville above any of the others. To be certain, Melbourne has many other attractions to consider if your visit is restricted to a single day.