I thoroughly echo the recommendations in Port Douglas and Palm Cove though I would not suggest the town centre of Cairns (Shangri La and HolidayInn) for a honeymoon. It is too much of a tour group and backpacker destination IMO.

Another consideration would be Thala Beach Resort, set in a very natural environment on a headland above it's own beach about 15mins south of Port Douglas. Accommodation is in pole vaulted bungalows scattered through eucalyptus bush with great views across the coral sea. It is a little remote though and a car would be handy.

If you can make it balance with your budget staying in more modest accommodation on the mainland, 3nts on Lizard Island would be sublime.