Tony,
Here are my recommendations for Austin, wine-centric dining, no particular order:
Aquarelle (french), Wink (eclectic), Zoot (eclectic), Paggi House (eclectic), Trio (steak/eclectic), the Carillon (eclectic), Asti (italian), Fino (spanish/mediterranean), Mirabelle (eclectic), Chez Nous (french brasserie), Fabi & Rosi (french/european), Max’s Wine Dive (southern comfort food)
Aquarelle, Wink, Zoot, the Carillon, Mirabelle, Chez Nous, Fabi & Rosi, and Asti allow you to bring your own wine.
The only ones of these that are “new” are the Carillon (which is on the UT campus), Fabi & Rosi, and Max’s Wine Dive.
Also, Ranch 616 (southwestern), Lambert’s (nuevo BBQ), and Garrido’s (tacos) are very good, but not particularly wine centric.
For true barbeque nirvana, go to Lockhart (about 30 minute drive south of Austin) and eat at either Smitty’s or Kreuz’s. Both are the best BBQ you will have. Ever. Anywhere.
And, for Tex-Mex, I recommend Maudie’s or Matt’s El Rancho. I’m not a fan of Chuy’s.