Hearsay on Travis @ Congress is open until midnight. Maybe Cabo, also on Travis. Most places shut down after 10 during the week.
There should be crappy chain theme restaurants or a Buffalo Wild Wings that's open just past midnight. It seems like some of the fancier hotels might keep their restaurants open late, although that might just be for room service. This Clayton's place out on the Beltway was the only thing I could see quick.
Just get the hell out of downtown. 2nd vote for Hearsay. But if you're not drinking their awesome drinks then you're wasting your money.
Not that it's any good, but the Buffalo Wild Wings on Gray two blocks from downtown is open until 2am most nights, midnight on Sundays/Mondays. Spanish Flowers on North Main, decent Tex-Mex, is open late. Probably your best bet.
Spanish Flowers is pretty nearby and open 24 hours. Plenty of stuff open around downtown, you just have to know where to look.
Tapatia on Richmond, thought not that close to downtown. El Rey closes at 3am. And I second One's a Meal.
I just assumed the OP was avoiding the "dining" copyright lawyers. Spoiler <iframe title="YouTube video player" width="480" height="390" src="http://www.youtube.com/embed/jvkgKRMlp90" frameborder="0" allowfullscreen></iframe>
