there is a good chance you will get a boat in our peak season, i kind of meant if you were traveling here for a few weeks and you really wanted to dive i would book ahead.. i would hate to think you came all that way and missed out on seeing the best of the gbr because it was booked solid for the short time you were here.
this site is proberly the best for comparing pretty much all of the boats around Cairns (including Port Douglas)
http://www.divingcairns.com.au/home.html
the best dive sites are the ones you can visit yourself..... but for commercial dive sites i would recommend ribben reefs as the most 'southern' reefs to visit
taka does a good ribbin/cod hole/osprey trip but any of the dive boats are very professional and will take you to the best of the commercial sites (remember the GBR is a wonder of the world and is heavily regulated in reguards to its use, 95% of visitors can only visit 5% of the reef)
if you like a good shark feed go to osprey! osprey is an awesome dive (1km drop off, 10-15m reef, lots of pelagics and good vis.. just an awesome site)
december is pretty much the end of our good dive season.. just before the wet hits.. very warm water and decent vis, june is the middle of our 'winter' 15 deg c at night 25-27 deg during the day! most Cairns locals are covered in layers of jumpers.. and the tourists are walking around in shorts and t shirts!
water is a little colder but its always awesome to dive, (you might go to a 3-5mm wettie during winter and i usually wear nothing during summer)
remember we have a wet season and a mild season, but it rains year round, (we are in the tropics) sometimes you will get 6 months of sunshine though and you wont even notice its raining at night, other times it might rain during the day. During the wet season, (now) it rains non stop for weeks when its not raining its overcast and humid. the runoff and heavy weather stirs up sediment on the exposed sandy reefs dropping vis to 5>m, however during winter with the weather being milder and more stable the vis on all the reefs is excellent (A locals tip... best time to go to the reef is when the planes are landing over the city, means the northerlies are blowing.. after a few days of this the reefs are dead flat and vis goes for miles!)
also if you get a chance i would try to visit townsville (3 hours south of Cairns by car) and get on a boat to visit the Yongala, considered by many to be one of the best wreck dives in the world!