If you look hard enough, there is heaps to do in Darwin. The Mindil Beach Markets on Thursday or Sunday nights are a must. Fishing is pretty popular, or you could try fish-feeding at Doctors Gully. The Darwin Museum is interesting if you want to know more about Darwin's history (such as Cyclone Tracy), as well as East Point Reserve, which has some great views. For eating out, the wharf is cheap and has great views of Darwin Harbour. Cullen Bay has more upscale dining and great harbour cruises. Shopping in Darwin mostly happens at Casuarina Square, but there is also Darwin City Mall or many of Darwin's markets. Another place good for tourists would be crocodylus park, great for getting close up to crocodiles and other Darwin fauna.
Quick Tips:
The best place for accommodation would have to be in Darwin City. Shops and other tourist sites are within walking distance, and it is the place for Darwin's nightlife. Cullen Bay also has some very nice accommodation. If you are in Darwin, I would definitely recommmend taking a day trip to Darwin's outer regions--Berry Springs and Litchefield National Park have beautiful sites for swimming.Best Way To Get Around:
Hiring a car is probably the best way of getting around--there is only so much you can see by walking, and you will definitely need a car if you want to see some of the spectacular sites further out of Darwin. If you are looking for a cheaper option, Darwin's bus service is pretty efficient--most are air-conditioned and leave every quarter of an hour. Taxis are another form of transport but are usually pretty expensive, and you will probably have to wait a while for them to arrive.