Port Douglas Hotels
I have had friends stay at Coconut Grove, which is on the main street of Port Douglas, about 5-10 minutes walk from the "action". The problem will be three bathrooms I think not the three bedrooms. Be prepared for sticker shock as everything is expensive in Australia.
Here is a link: http://www.coconutgroveportdouglas.com.au/
But if you Google holiday apartments Port Douglas you'll come up with more.
If you are not going to have a car, then I would strongly recommend that you find accommodations in the town itself or within walking distance of the town. I believe there is a private bus that operates from the hotels located at some distance from town, but it's expensive and time consuming.
A good resource for finding serviced apartments and reading reviews of them is on Trip Advisor. If you are not familiar with their site, go to the Australia forum. The select "Port Douglas" under "Jump to a more specific forum". Then go to the top of the page and click on the Port Douglas tab. Click on "Port Douglas Hotels" and then select "Specialty Lodging". You'll find reviews of 52 different serviced apartments.
Hope you enjoy Port Douglas as much as we do. Also, if you intend to visit the Great Barrier Reef we have also done this (again several times) through Aquarius cruises. They visit the Low Isles where we swam with the Green Turtles - just magic.
Celebrity: Silhouette 10/11/12; Solstice 6/28/13; Solstice 11/4/13; Century 4/26/14
Royal Caribbean: Viking Seranade 1/2/95; 3/28/97; 4/2/99; 4/21/00; Rhapsody of the Seas 8/01; Monarch of the Seas 4/04 3/05; Jewel of the Seas 8/15/08; Radiance of the Sea 11/7/09; Serenade of the Sea 11/7/10; Voyager of the Seas 3/24/12; Quantum of the Seas 4/12/15; Serenade of the Seas 10/7/15; Navigator of the Seas 9/18/16
Carnival: Elation 4/98; Fascination 6/00; Ectasy 4/02;12/05; Conquest 3/03;
Princess: Coral 6/03; Sapphire 12/04; Sapphire 9/11; Golden Princess 11.14
Radisson: Paul Gaugin 8/02
Premier: Big Red Boat 8/90