marschall the are heaps of places to ride, and here are some resources also.
http://www.mtbfreak.com/default.php - local info, reviews, news and discussion boards.
http://www.insidelinemtb.com/ -local downhill club.
http://www.bikesa.asn.au/ the local lobby group - they do good work...
http://www.amtbc.com/content/default.asp -local XC club.
I live in the hills and am quite close to some great trails in Sheppards Hill Reserve. It has excellent singletrack an fire trails and is legal. You can get to it by train from the city, just get off at Eden Hills and start exploring! [ Best to look at a map first...]
Sturt Gorge has some good trails also, just off the back of Bellevue Heights.
Also, all State Forests are legal to ride. Try looking at any of the Kuitpo Forest areas near Meadows, or further north, Mt Crawford Forest. [ Need a car ]
Belair National Park, Cleland Conservation Park, and Andersons/Randells Reserve are all quite close to the city with awesome riding, but are now illegal to enjoy on a bike.... bummer.
Bike SA with others have built and mapped a network of trails in the Cudlee Creek / Fox Creek area. Its further north in the hills, on the way to Gumeracha from the city [ need a car ] Awesome trails.
You could consider the Mawson Trail also. Mostly fire roads but still good fun.
It goes from the city to Blinman in the Flinders Ranges!
http://www.southaustraliantrails.com/top_trails.asp?mawson
Dont know about the Barossa, but i think the Mawson trail goes throught there on its way to Burra.
Happy trails!