The Stuart Highway is the only sealed option. Drive North, you will reach the tropical Northern end and Darwin. To the South, you will enter South Australia, with Adelaide at the end of the road.
If you have a 4WD, you can cut Northwest directly to the Kimberley on the Tanami Track, a relatively well graded dirt road crossing the Tanami Desert. It is a 800+km drive to Hall's Creek in Western Australia, with very little supplies along the way, and only a single fuel station at the remote Rabbit Flat Roadhouse which is not open all the time, on top of that, roughly midway between Alice Springs and Hall's Creek.
To the West, you can take the unsealed Gunbarrel Highway starting at Kata Tjuta, and with a lot of patience and a good 4WD you could drive all the way to Perth something like 2500 km away.
To the East, the WAA line or the French line are 4WD tracks crossing the Simpson Desert to Birdsville in Queensland, some 500 km East. Be extremely well prepared if you wish to tackle those routes.
Coober Pedy â spend the night in an opal mine
Darwin â The tropical capital city
Katherine â nature and culture, history and heritage, and gateway to the spectaular Katherine Gorge
Tennant Creek â Aboriginal culture, gold mining and pastoralism
