I just come back from a cycle tour in SA, did the Mawson Trail, great track, it starts in Adelaide and heads up through the Flinders Ranges. Great mountain biking at the mtn bike park at Melrose, the guys at the bike shop there organise a ride at 7.30 every morning for who ever is around. They are really helpful and keen to show the trails. Great caravan park in Melrose, great little town to spend a few days. Rode through the crawford park closer to Adelaide, this looks good, lots of trails there. Lots of mountain biking around Wilpena Pound.
Enjoy your trip, its a great place to ride!!!