Everyone that visits the far north coast of Queensland wants to experience the Great Barrier Reef. In my opinion, the best place to do that is the Whitsundays which are below Cairns.
But if you only get a chance to go to Cairns and you are on a budget, then you need to choose Fitzroy Island. A day trip to Fitzroy from Cairns is just a short ferry trip away and is cheap.
You can also visit the turtle conservation area on the island and find secluded white sand beaches. The main beach is made up of little shells so you will need coral walking beach shoes. Cairns gift shops sells them cheap.
Fitzroy Island has a beach bar surrounded by tropical gardens and awesome views overlooking the Great Barrier Reef.