For dinner we recommend one of the restaurants in the Cairns Marina, the Italian Marina Paradiso (Tel +61 7 4041 6969). The views are great, it's a peaceful place with good food. 18-20 AU$ per dish.
For something cheaper, at the corner of the esplanade and Aplin St. is another Italian restaurant, Villa Romana, where the food is also delicious. Here we recommend the Penne boscaiola and the fruti di mare pasta.