The Nitmiluk National Park ranger station in the Nitmiluk Visitor Centre has maps of available "bush campsites" throughout the park. These are very basic sites -- no showers, no soaps or shampoos allowed (they pollute the river system), and simple pit toilets or none at all. Most are beside natural swimming holes. You must stop for a camping permit at the ranger station beforehand; the camping fee is A$3.30 (US$2.65/UK£1.30) per person per night.
There are caravan and camping sites at Springvale Homestead (tel. 08/8972 1355 or book through Travel North), 7km (4 1/3 miles) from Katherine township on the banks of the Katherine River. Sites are in a shady park, and there's a licensed bistro and kiosk, swimming pool, and children's water slide. Wallabies roam freely. Fees are A$9 (US$7.20/UK£3.60) per adult, A$5 (US$4.40/UK£2.20) per child for a tent site, and A$23 (US$18/UK£9) double for a powered site (A$9/US$7.20/UK£3.60 for each extra person).