While you're in Austin, you need to try good ole Texas barbecue. While Terry Black's isn't the most popular of Austin's barbecue options, it is one of the easier to get in and out of in a more reasonable timeframe. Try the beef rib.
If you want to take an all-day excursion to try barbecue, Franklin Barbecue is the place to go. It is consistently rated the best in Austin (John agrees), but you will also spend at least 3-4 hours standing in line. I doubt many of you hungover wedding guests will want to stand in line for that amount of time... but if you brave the line, the payoff is worth it.
When it comes to Tex-Mex, Matt's is an icon in Austin. This restaurant has been around forever and is one of the Walton family's favorite places to eat in town. Try the Knockout Mexican Martini. Beware, you're only allowed to order two of them during your visit for a reason.