In the Simpson Desert you will find some of the best four-wheel driving in Australia. Literally take the four-wheel drive (and plenty of water) off road.
The Binns Track runs parallel to the Stuart Highway from South Australia to Timber Creek, NT where it connects with routes into WA. Old Andado Track follows the desert's western edge to the town of Finke. It's challengeing driving, so be well prepared (check fuel and double check water). There's rolling sand dunes and hilly terrain. But take the path knowing this desert territory that has been seen by very few (western) people.