Driving is the best way to comprehensively see Darwin. Many of the sights are spread out, parking is easy and traffic is usually free flowing.
There is a public bus service (http://www.nt.gov.au/tran...), which is useful for accessing areas close to the city. The services are more frequent closer to the central area where the routes overlap, but you will need to plan according to the timetable to get anywhere else - some services only run a couple of times a day. The buses are air-conditioned. $2 per 3 hour transfer or $15 for a weekly pass.
Walking between attractions or from a bus stop to attractions, even in the inner-city, can be very hot work for those not used to the Darwin climate. Dress to stay cool, and carry water.
Tours are available, and tour coaches are available to some attractions.
Buslink
Buslink are the major private provider of public transport, operating half of the Darwin Bus Network. Buslink also have charters.
Darwin Private Hire Cars
Darwin Private Hire Cars specialise in corporate and leisure transportation, and airport transfers. With a full range of personalised transport options to suit your specific needs, the driver/guides are fully trained so you can enjoy your outback experience.