By car
The Northern Expressway provides direct access to the Barossa from Adelaide. It is a 110km/hr, limited access freeway. From Adelaide take the the Port Wakefield Highway A1 to the north, then onto the M20 motorway, bypassing the town of Gawler and entering the Barossa at Greenock in the Northwest of the valley. Allowing 60-75 minutes between the airport and Barossa winery tasting rooms is realistic.
Getting to the Barossa from Adelaide or the airport is considerably easier than traveling to Australia's other major wine regions Hunter Valley from Sydney - about 2-1/2 hours; Yarra Valley from Melbourne - about 1-1/2 hours; or Margaret River from Perth - about 3-1/2 hours.
The scenic driving route to the Barossa is via the Adelaide Hills just East of the city, and then North through the hills enjoying country roads and sleepy towns. Perhaps drive through Inglewood Houghton and Williamstown to arrive in the Valley at Lyndoch. If time permits, the whispering wall, a reservoir wall at Williamstown is worth a visit. Similar to the sound effect in the dome of St Pauls London, but on a far far larger scale, whispered sounds, inaudible a few feet away are miraculously focussed by the wall to be perfectly audible half a kilometre or so away.