Have a look at
www.greyhound.com.au as they have a Darwin to Kakadu service for about $35 one way and
www.yha.com.au have two hostels, one being owned by aborigines and a good bet they would be able to organise to get around a bit and the other at Cooinda mentions fishing tours.
Might even be worth it to have a night or two at each.
You might even find in Darwin, quite a few hostels all close together in Mitchell St., that there could be people looking for others to share petrol