Lobethal Bierhaus (
http://www.ahcb.com.au/) is definitely worth a visit if you can get up to the hills. Grumpy's (
http://www.grumpys.com.au/) as well, although I haven't been there in a while.
The Brew Boys in Regency Park (
http://www.brewboys.biz/) should have a cellar door open from early December which would be worth a visit.
The Port Dock Brewery Hotel in Port Adelaide (
http://www.portdockbreweryhotel.com.au/) is OK if you're out that way. The Holdfast in Glenelg... not worth it in my opinion.
I have heard good things about the Steam Exchange in Goolwa (
http://www.steamexchange.com.au/) but am yet to make it down there.
The King's Head in the city has a lot of SA brews on tap and in bottles as well.
And of course, no trip to Adelaide is complete without a visit to the Wheaty (
http://www.wheatsheafhotel.com.au/) in Thebarton.