I stayed at the Sheraton Mirage Port Douglas, nice hotel just abit out of town. Nice and quiet, huge pool, friendly staff, the grounds are well kept.
Alternative, Peppers Beach Club close to shops beach.
My main choice where I have stayed, is Palm Cove just down from Port Douglas. Beautiful little place, lovely accommodation most of which overlooks the beach, lots of eating places, has a great upmarket pub which is clean and nice which has great meals.
My choice of accommodation at Palm Cove , Sea Temple Resort and Spa, or Peppers Beach Club.