I haven't flown around Darwin for a few years now but there used to be a pink and purple C177RGII on cross hire to DAC a couple of years ago. When I was there a few weeks ago it was still on the tarmac (I think - might have been through nostalgic beer colored glasses though!), but it might still be available for hire? (haven't been flying in Darwin for a couple of years.
Places to see. I used to take friends over Twin Falls, Jim Jim Falls Litchfield, along the coast around Dawrin around dusk, and Elliot falls. And of course you have Katherine Gorge. Don't let the local sight seeing companies push you around by saying you aren't allowed to fly in these areas below XXXX ft. As long as you follow the fly neighbourly in the ERSA you can't go wrong. Can fly into Jabiru for a bit to eat and a drink. Some very beautiful scenery. It was hotter but better in the wet when the rivers were in full flow and the falls were all magnificent. The air was also clearer and if you go in the mornings and back by around 1400 local, not too many cloud build ups to dodge!
Cheers
Jards