Darwin has an extensive public bus system that services most suburbs from the inner city to Palmerston. As a student (concession), you can purchase $1 tickets for three hours of travel, or better still buy a weekly ticket for only $7.
Flat terrain and cycling paths make for easy, safe, walking and cycling in Darwin and surrounds. More information on Darwin's bicycle paths can be found on the NT Government.
Driving a car or motorbike is another option. Alternatively, Uber and other ride-sharing services are also readily available in Darwin.