Hands down... my favorite place for Sunday brunch in Austin is the South Congress Cafe (note that they serve brunch every day of the week). The restaurant is also a great place for lunch or dinner, but I love hitting the SoCo Cafe late Sunday morning after a bike ride or a run.
You can expect a wait at this popular restaurant on the weekends but you can grab drinks at the bar (and eat at the bar if you're lucky enough to score a seat) and you can leave your mobile number with the hostess if you want to go explore the neighboring boutiques on South Congress Ave that are super hip.
The SoCo Cafe serves the best bloody mary in town made with their Titos infused vodka. My favorite dish is the "migas" but you can't go wrong and the specials are always creative and good.