I live in South Australia, but have family in Darwin and have travelled a fair bit around Australia
If you can, go to the Bindi Beach Markets, they might be closed for the wet season by the time you get here, but they are awesome. Right on the beach, awesome foods and homecrafts.
Also, go to eat on the warf. You sit right out on the end of the warf in the ocean. The seafood is awesome, and you can watch the fish swiming by just by looking down from your table. Beautiful.
If you are interested in that sort of thing, the Darwin War Museum is very interesting. Darwin was bombed in WW2, and had lots of military movement. In fact, as you drive around near Darwin, you can see the abandoned airfields everywhere.
Make sure you drink lots of water and really keep hydrated. You will be arriving at the start of the build-up to the Wet season so it will be very hot and humid. You will sweat a lot more than you realise. The people in the Territory are very very friendly, dont hesitate to start up a conversation with the locals, they will be able to tell you all the best places to go, see and eat.
Do take care around the water. There are natural springs you can swim in, but watch for Croc signs and stay out of the water where they are posted. Litchfield National Park is only about 2 ish hours from Darwin and very beautiful (they filmed Crocadile Dundee there). Make sure you take plenty of water and let people know where you are. There is a LOT of open space in the Territory with no-one for miles and miles.
I have done The Great Ocean Road as well. Take advantage of all the little viewing spots, the views are amazing! Pt Fairy is lovelly, the caravan park is very nice, with big BBQ areas available for free. If you are eating in Port Fairy, avoid the big White Pub. It looks lovely, but the food is dreadful. Try the little pub directly across the road.
Also, I second Taronga Zoo and the harbor ferries. The ferry is pretty heap, and its like a tour all of your own. The Zoo was great as well.
Most of all, have a blast! Us Aussies are very friendly and polite as a whole, and love showing tourists our beautiful country.