Right in the far north of the country, lies the capital city of the Northern Territory. Its location, close to Indonesia, makes it one of the most Asian towns in Australia. There are many Asian tourists here, and lots of Asian eateries.
There is a lack of major attractions in the town itself, but the laid-back atmosphere, and the tropical settings, makes it a good place to visit. There are plenty of restaurants and nightlife to keep you amused in the evenings.
But the major attractions lie out of the city, in the form of national parks. Litchfield can be done as a day trip from the city and boosts huge termite mounds, tropical scenery, and natural pools near beautiful waterfalls. The most famous national park is probably Kakadu, with beautiful tropical scenery, creeks, more waterfalls, crocodiles, and aboriginal heritage.
Quick Tips:
Book tours to the national parks in the hostel you are staying. They should be able to work out your wishes and translate them to a tour with acceptable prices. The hostels normally work independently from the tour companies, so they will not force you to use a tour that you don't really like.
There are plenty of live music bars in the city centre, and plenty of places with Asian or Western cuisine, so you won't get bored very easily during the evening.
Best Way To Get Around:
As long as you stay in the city centre, keep on walking. The hostel/hotel you are staying in will most probably be located in the centre anyway—the Darwin nightlife is never far away.
To get further away, there are buses going all directions and to the international airport as well. If you want to visit one of the national parks, you can either, rent a car or a camper van or go with an organized tour. Last, but not least, from the harbour and from the marina you can take boat trips, like on Port Darwin bay.