If your budget is not great then eat in Grant St - the little Thai shop there has the BEST food at a great price, and all the other eateries along there have great budget options - pizza, kebabs, salads, pies, vegetarian food etc.
Otherwise the Tin Shed (Port Douglas and Districts Combined Services Club) and Yacht clubs are both fantastic places with incredible views and good food and you can mix it with the locals there.
Wrapz Cafe across the road from Coles is great for lunch. As is Taste on Macrossan Deli. And Otz Cafe out at Four Mile Beach Shops.