Darwin is a city in Australia.
From Darwin, you can really only go South. The first town you will hit is Katherine. It is advised to take the bus to Palmerston ($2.00 for a 3 hour ticket as of April 2011) and then simply walk along Temply Terrace to the Stuart Highway, about 1km away. Traffic is slow at this point and there is a set of traffic lights. You may get very lucky as there is plenty of long distance traffic going past here.
Darwin is in the Northern Territory, which means sleeping by the beach is not a great idea due to crocodile danger.