If you have the time to spend actually at the reef, then the best way to go is to actually sleep out on the reef on a live aboard vessel, instead of coming back to the mainland to sleep and eat.
Not only does it work out cheaper than a series of day trips, it also gives you a lot more dive time at various locations, and best of all you get the opportunity to do a night dive.
Organised trips range from 2 to 7 days, and private charters can be arranged for even longer periods.
The local live aboard operators offer different things and go to different places, so think about your own needs (and those of your travelling companions) and choose for the trip that suits you.
Pro Dive Cairns offers a personalized liveaboard experience on three purpose-built dive vessels, exploring up to four rarely-visited Outer Great Barrier Reef locations