If you travel to Cairns from outside of Australia, there are limited options for flying straight to Cairns from overseas. Direct flights to Cairns are from Singapore, Japan, and Auckland in New Zealand.
Given the contrast between the wet and dry seasons, you might think May to October is the best time to visit Cairns. As a rule, this is the case. Not only is the weather beautiful, but you also do not have to worry about marine stingers that are around in the wet season.