I dove at Lady Elliot Island, which is about as close to Brisbane as you can get and be on the GBR. You have to charter a plane from Brisbane, Bundaberg, or sometimes other locations and it’s a small island with one eco-resort. Snorkeling is fabulous there. I saw a black tip reef shark in the two days I was there. There are many dive sites including shore dives and short boat rides (10 minutes). They even have nice reef wading trails where you can see giant clams and a variety of fish and corals without even having to swim (good for kids).
I’m sure the rest of the GBR is fabulous too. You can’t go wrong. Townsville and Cairns are the major launch pads for taking boats out to the reef from the mainland.