Things to Do in Katherine
Nitmiluk (also called Katherine Gorge) is the deep path cut through the sandstone by the Katherine River, and the Nitmiluk Katherine Gorge National Park is where you can go to lap up the luscious experience of the Gorge, whether that be swimming in it (sometimes with harmless freshwater crocodiles), canoeing in it, hiking around it, gazing it from an observation deck, flying over it on a helicopter...or any combination of the above.
The park is run by the traditional owners, the Jawoyn, in conjunction with the Australian government. It's a well-appointed place with lots of visitor facilities (and lots of visitors, especially in the dry season). You can choose your level of activity, from lounging around at your campsite or the visitor center café to strenuous canoeing trips or hikes. But make sure you take at least one long hike, perhaps to see the Aboriginal rock art, or at least to get sticky enough to make cooling off in the river a delight.