As with much of Cairns, you can divide the city into the Esplanade and the places within a block of it, and the rest of the city. The Esplanade is littered with bar and grill places supplying red meat and beer all in the one place, and with seafood restaurants. It's relatively difficult to find anything open before 11AM, since they expect the clientele to be sleeping in. The rest of the city has small cafes and milkbars catering to locals. The number of Japanese tourists here makes Japanese food a fairly reliable option, although prices can be steep.
A number of the more expensive restaurants on the Esplanade, particularly towards the north end, offer discounts of 20-30% for early birds: usually you will need to order by 6:30PM and pay and leave no later than 7:30PM to get a discounted meal.