Cooktown's superb tropical climate ensures that which ever month you visit "is a good month". The period from April to December where rainfall is at its lowest is enhanced by fresh tropical breezes. With daily sunshine averaging around 7 hours, and a maximum average temperature of around 27oC your visit is assured the perfect conditions. The Wet Season from January to March provides the best time to see both rainforest and outback savannah in all their glory.
For more information on the weather, visit the link above or the Bureau of Meteorology.
The climate averages for Cooktown see: Readings for Cooktown Post Office - 031016