It's always a debate amongst my friends as to which restaurant we should go to to sober up at: Magnolia Cafe or Kirby Lane. While both restaurants are equally good, any Austinite (or transplant) who has spent any time in the bars inevitably has a preference for one or the other. Having been born and raised in Austin, hell, I like them both.
I've always liked Magnolia's mint hibiscus tea, but my favorite dish on their late-night menu is the "Eggs Zapatino." This is essentially an english muffin topped with a ham, a generous helping of scrambled eggs, and queso (cheese). It's kind of like an Egg McMuffin, only much, much better.
The fish tacos are pretty good, too, but they are nothing like the ones you can find at west coast joints like Wahoo's.
The rest of the menu is standard late-night Austin fare: eggs, pancakes, sandwiches, tacos, fajitas, and quesadillas. Everything is pretty good, but (perhaps it is because I'm Asian and a snob about these things), I can't condone their "stir-fry."
One suggestion: try to get there right at 2am (leave the bars early) or after 3am, because the wait can get long just after the bars close (especially at the Lake Austin Blvd. location).
Also, tip your waiter/waitress generously--they are working during the middle of the night.