Part of the attraction of Adelaide is that it is a compact planned city. Even though its population is over 1 million it is easy to drive into the city centre and get a car park (without paying an arm and a leg for it).
Some things that come to mind:
Stroll along North Terrace in the city (museum, art gallery, etc.).
There is great driving in the Adelaide Hills - a maze of interesting roads (Classic Adelaide tarmac rally runs on some of these roads every Nov).
The old Adelaide F1 street circuit gets used every year for the Clipsal 500 (V8 "Supercars"); in late Feb this year.
Catch a tram from the city to Glenelg and the beach.
Hallet Cove on the south coast.
Day trip to Victor Harbour on the south coast.
Murray River / Riverland / Goolwa / Coorong ("Storm Boy").
Kangaroo Island.
If you want to get the "Outback" experience, head north, e.g. to Coober Pedy.
And there are several RFs in Adelaide - perhaps one of the owners will supply contact details.