Twin Falls flows year-round (no swimming), but half the fun is getting here, involving a little boat trip (adult/child $15/free, 7.30am-5pm, last boat 4pm) and an over-the-water boardwalk. The falls are reached via a 4WD-only track that turns south off the Kakadu Hwy between the Nourlangie and Cooinda turn-offs. Twin Falls is about 61km from the turn-off. The track is open in the Dry only and can still be closed into late May; it's off limits to most rental vehicles (check the fine print).
A couple of tour companies make trips here in the Dry.
