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www.diversionoz.com.
These guys really know their stuff, they personally go check out the liveaboards and reefs visited and then report back on the website.
If you have an idea of which reefs you want to go to, send them an email and ask them to suggest a dive operator and a fun itinerary for you.
I met Phil who works for Diversion Oz on a liveaboard out of Townsville last year going to the wreck of the Yongala. He seemed like a genuinely nice guy and really knew his stuff!
It is all done in Aussie Dollars so generally you'd probably get a much better deal for your hard-earned dollar.
If it fits your itinerary I'd recommend doing a liveaboard with "Undersea Explorer". They are based in Port Douglas and dive up near Osprey Reef and the Cod Hole/Lizard Island.
For Day Trips out of Port Douglas, I'd suggest Taka Dive or Poseidon Dive. You'll probably see Quicksilver Dive advertised a lot, but personally I found that they had waaaaay too many people on the boat and it seemed more like a cattle call then a great dive boat!
The Diversion Oz website also lists Day Trips out of Cairns & Port Douglas so that should give you some idea.
I'm from Sydney but for the last 12 months I've been living in North Queensland (few hours south of Cairns) so if you have any further questions about Sydney OR Cairns/Port Douglas send me a PM.
Good luck planning your trip!