Hi M.,
We moved to Austin this past July. What we did was go to church. I just started women's study last night and found out a lot of families home school and they set up a weekly play date where all families (not just homeschoolers) are welcome. So I plan to do that with both of my kids since it's in the afternoon after school. Maybe get plugged in that way? Send me a note if you'd like a copy of the info.
There is also a web site called meetup.com that I've not used but I see it often recommended. If you have a hobby or want to hang around other moms, there is probably a meetup group you can join.
If you are looking for some way to meet people that's less formal, you might want to try parks. They're all around town and the ones that I have found are pretty busy (looks busy with moms' groups). My short list: Circle C park west of Slaughter and Escarpment, Dick Nichols park off Beckett, and Zilker Park playground which is free to park during the week ($3 I think on weekends). I know there are others but I've not found those yet.
I hope that helps! Austin's a pretty friendly town so no doubt you'll get plugged in soon.