While Cairns is a nice, relaxed touristy town, there's not a huge amount of things to do in Cairns itself. Apart from the Casino, shopping, markets, restaurants and one museum, things to see and do are around the city. Kuranda can be reached by Skyrail and a tourist train, but other places such as Port Douglas, Mossman, Daintree Rainforests and Atherton Tablelands can only be reached by car unless you go on an expensive tour. So it is likely that you'll be looking for a vehicle to rent. All the places above can be reached by a 2WD car. If you drive further up north to the Cape York peninsula, you will have to hire a 4WD vehicle.
Courtesy of Tourism Queensland
The common, large, places to rent a car are Hertz, Maui, Thrifty, Britz, Apollo, Avis and Europcar. While many backpackers rent Wicked vans or buy and sell old campervans, it is not a safe option as they can break down and there will be nobody to ring to come and give you a hand. Large companies are a bit more expensive, but they do one-way rentals, offer mechanical assistance in case you break down, and you know what you get.
NOTE: This website is written in British English, which is the English we use in Australia. You will find words like "traveller", "harbour" and "realise", and they are all correct in the language used in Australia.