Direct_to - Housing and accommodation in Darwin is exceptionally tight, despite a major building boom. This applies equally to both holidaymakers and permanent residents. The NT is undergoing boom times, with gas projects, and mining, both going gangbusters.
Don't expect to find anything under about $160 a week, and $200 isn't unusual. Darwin housing is some of the priciest in Australia - for what you get.
Pick your suburb carefully, some areas of some suburbs are pretty rough, and the drunken, fighting indigenes can be a right nuisance - despite the NT Police Force being pretty hard on 'em.
Start with Google, and I'd recommend Gumtree initially. Move fast when you see something attractive, and advertised recently.
room to rent darwin - Google Search
Find house rental, unit and apartment rental opportunities in Darwin - Gumtree Free Classifieds - 1