Most of the Austin breweries only have open houses a few times a year. Independence does one once a month on a Saturday. Real Ale in Blanco is open every Friday for free tasting and tour.
There are quite a few brewpubs in town though. The drafthouse is a well known on in North Austin. They have a number of very good guest taps and usually 2 or 3 of their own brews. Uncle Billy's Brew and Que is a great place for lunch, they have 7 or 8 of their own on tap and once in a while they do a guest tap. They had a cask of Jester King beer the other night.
North by Northwest is a restaraunt/brewery but frankly I think they are more concerned about food than beer, their beers are ok but the food is excellent.
There is also Lovejoys and the newly opened Black Star Coop. Black Star just brewed their first batch a couple days ago so they dont have their own beer yet but do have guest taps. I have never been to lovejoys.
That should get you started