Although Cairns itself is not the largest city in the world, it is still a good idea to hire a car for getting around in order to see all the local attractions during the day, while at night, taxis are the best option for getting from your hotel to the nightclubs and bars that the city is famous for.
Many boat companies offer cruises out to the Great Barrier Reef, but if you don't have the time do indulge yourself like that, then without a doubt, the best way to see it is either from a seaplane, or on one of the helicopter tours that operate from the city.