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There are organised tours from Darwin or Jabiru which can lead you to Aboriginal rock art and awesome natural attractions.
It may seem unfortunate in non-Aboriginal eyes that not all of Arnhem Land is made more accessible for a better understanding of Aboriginal life and culture.
But this is their land, and it is their right to only invite those they please and only to a few selected sites.
In the north you can visit, with the necessary permit, Sandy Creek and Wunyo Beach, fishermen's haunts in a setting of pristine natural beauty, both able to be reached by four-wheel drive. Danger lurks here as well in the form of saltwater crocodiles, familiarly known as salties, which attack even when unprovoked. And no, you cannot kill them, they are a species protected by law.
On the Gove Peninsula, in the east, you can fly without a permit to the town of Nhulumbuy. But if you travel overland from Katherine, a permit will be required.