The good diving sites in Great Barrier Reefs are all quite far out (such as Cod Hole) so you need to do live-onboard either 1 night or better yet, 2 nights, to properly do SCUBA.
Daytrippers are better for snorkeling as the coral reefs are very close to the surface - in fact, at low tide, you need to be careful for reef-cut.
Of my head I dont remember the operator's name but we were very happy with our daytrip out from Cairns.
Dont go with QuickSilver - they are too famous too big - very crowded boat and they go out from Port Douglas eventhough they would come to Cairns for pickup.