There are four main roads leaving Alice Springs: the Stuart Highway, which runs north to Darwin and south to Port Augusta; Larapinta Drive which runs West and splits off to the Namatjira road; and the Ross Highway, which runs East. The Stuart Highway highway 87 is sealed all the way; this means it's got tarmac and is passable using a normal car. Larapinta Drive and Ross Highway are sealed for a couple hundred kilometers in each direction, but after that they convert to dirt roads which you will need a 4x4 vehicle to access.
There is a web of dirt trails - sometimes called unsealed roads - which surrounds Alice Springs, and some of the nicest places within a few hours drive will require a four-wheel drive vehicle 4x4 to get to. There are two ways to go south. The first is the Stuart Highway, which is sealed and frequently traveled. The second is a dirt track which leads off the Stuart Highway; it's called the Old South Road. A dirt track connects the Old South Road to the modern Stuart Highway, from a point north of the aboriginal community of Titjikala.
On the side of the old South Road, you will see a narrow track that follows the road - this is the track of the Finke Desert Race which is held every year on the Queens Birthday Long Weekend in June. Best to just view the track though and not drive on it as it is VERY tough going, even at low speeds. If you are game and drive on it, have a think about how the competitors race along it at speeds in excess of 150km/h on race weekend.
further north
Tennant Creek - a small town, makes a great base for seeing the Devil's Marbles and the Pebbles.
further south
Coober Pedy - the home of opal mining in Australia with underground hotels
Mount Conner
a plateau frequently mistaken for Ayers Rock by travelersUluru-Kata Tjuta National Park - home to Australia's most recognisable natural icon
Watarrka National Park - home to Kings Canyon, a mighty chasm reaching a depth of 270 metres with some great options for the less energetic to explore
around alice springs
Chambers Pillar Historical Reserve - a spectacular solitary column towering 40 metres above the Simpson Desert plain
East MacDonnell Ranges - following Ross Highway, you'll find plenty of gaps, rocks and gorges
Ewaninga Conservation Reserve - gain insight into an ancient culture as you explore the small, six hectare Ewaninga Rock Carvings
Jim's Place
an outback roadhouse with Dinky, the singing dingo. Next door to this property is a great camel farm, tooRainbow Valley - a scenic natural reserve consisting of various formations of sandstones and rocks
West MacDonnell National Park - Simpson's Gap, Glen Helen Gorge and other stunning gorges and rock formations