Hi
If want a liveaboard although the time you have sounds too short, three days needed, try:
The spirit of freedom
http://www.spiritoffreedom.com.au/
It is the high end side but well worth it. It is an amazing liveaboard.
taka dive
http://www.takadive.com.au/
It is cheaper, (than the spirit but so is my car), but doesn't mean its cheap. Amazing boat, great food and great people. You will meet some great people from around the world on there. These guys have been around a long time and know what there doing.
For a day trip I would go with Quicksilver Dive. They have a couple boats. One for just diving and one that goes out to the pontoon so if you have others with you that do not dive this is the best option.
I love these guys and always have a great time on their boats.
http://www.quicksilver-cruises.com/
There is also Tusa dive for a day trip to the reef just off Cairns. You can find them on the esplanade and also pro dive near the wharf does day trips with them.
http://www.tusadive.com
After living and working in Cairns these are the guys I dive with and trust.
To be honest I am not a big Mike Ball fan. And I am not opening a debate here or anything like that.
To me and only my thoughts, I wanna support someone who supports the industry in a positive way.
I have heard his boats are nice and dives good, so you wont here my say there not. I just do not think I would dive with him. I guess I still have a bad taste in my mouth after the pricing problems he had.