While lots of people know about Cooktown because of its history, few are aware of the amazing diversity of wild landscapes to explore around the town - rivers, rainforest, sandstone escarpments, wetlands. But the country is not for the inexperienced bushwalker as there are few trails and no boardwalks. You can find out more information on the walks by following THIS LINK. Exploring that site shows more information on Cooktown, and they have a booklet on walks. However you need to talk to the locals to find most of the routes and to get permission to access certain areas whether owned privately or by Indigenous clan groups.
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