I disagree with the earlier comment about Port Douglas, which overall is a far more charming and pleasant town than Cairns. There's also more to see north of Cairns than in Cairns. I would advise renting a car, spend a night on the front and/or back end at the Hilton Cairns, and staying in Port Douglas (at the Radisson, near the Sheraton, we stayed in a two-story, two bedroom apt. unit last Nov. for a mere $110 US per night--call their 800#).
By all means visit the Reef, which can be done from either Cairns or Port Douglas. Also well worth seeing is the Tjupukai Aboriginal Theme Park between Cairns and Port Douglas, and the tropical rain forest nearby at Daintree Village. For an unforgettable hotel experience, book a night ortwo at the Daintree Eco Lodge where you stay in a specially built cottage on stilts in the middle of a rain forest (the only one in Australia). They also offer a sunset jungle cruise that is like something out of "Animal Planet." If staying there isn't feasible, go for dinner as the Lodge's restaurant is very good and will give you the flavor of the rain forest environment.
One downside you should know is that while there are beautiful beaches, you probably won't want to swim in them at that time of year due to jellyfish. You'll see nets set up to keep them out at public beaches but we were told they're far from foolproof.
For more info on the region, pick up a good guide book before you go; I recommend Frommer's Australia 2000.