We had to pay to get a shuttle into the city to look around as we were docked too far out of town for taxis. At this port we just did some shopping at the mall. There is also a free ferry (the Cityhopper) that takes you for a ride along the Brisbane River, the terminal is just a short walk from where the bus drops you off in town. This was nice but be warned it takes forever to visit all its stops and return again!
Cairns was lovely. Here we visited the Rainforest Station, Kuranda Village and did the gondola ride. Outstanding.
Don't miss the Tchou Tchou train shore tour! A very charming experience, I'm sure people of all ages would enjoy it, not just those with children. You get a fantastic tour of the island and some fresh French pastries and cold drinks at the top of a hill where you can also take in the views. Afterwards do some shopping when the tour guide drops you off in town. Shopkeepers will take small amounts of Australian dollars, otherwise take some local currency for larger purchases. Make sure you know where to get back on the bus to go back to the ship! I didn't and I got delayed lol.
We did the Great Barrier Reef shore tour here. It is very expensive, but we felt it was worth it to snorkel on the reef (something on our must-do list) and we really didn't want to organise this ourselves. It was excellent. There was a glass-bottom boat available as well and a buffet lunch. The only drawback was the 2 hour catamaran ride out to the pontoon. It was fairly rough and our youngest son was sick a couple of times, however the staff on the tour were very supportive.