I'm looking for a very particular type of venue. I'd like to find a
jazz club that I would describe as sort of "old fashioned" probably...
To give you an idea, one of those places where you can eat at tables
and enjoy a jazz show in a nice, upscale, 20's atmosphere. Now, the
requirement is that such a place be in one of these cities: Austin,
San Antonio, Houston or Dallas and that in the next two months at
least a show be scheduled which includes old-time favorites of Jazz
such as music by Cole Porter, Ella, Louis Armstrong, etc.
From the websites you find all three these elements should be somehow
evident. Remember, style/atmoshpere, location (TX) and music (Cole
Porter, Ella, Louis Armstrong, Nina Simone, Billie Holiday...) No new
jazz stuff. Thanks.

I'm not aware of any clubs or bands in Dallas that completely fit your
bill.  The places I've seen tend to be a bit more modern in style yet
still a nice, upscale supper club feel:
1.  Sambuca - catch it when Ricki Derek & the Vegas Six are playing. 
The vibe can get pretty ostentatious and glitzy, and on bad nights the
music is merely wallpaper.  The good nights are a more modern
adaptation of what you're after.  The band plays mostly Rat Pack
tunes, but Cole Porter makes a few appearances, too.  **DISCLAIMER** -
I play in the band, but we draw well there and get a decent response,
so I figure some other folks enjoy it.
2.  Beau Nash - try and catch it when Hunter Sullivan is playing.  His
scene is similar to the Ricki Derek thing, but I think his vibe is a
bit more of the sensitive crooning vs. the more raucous think with
Ricki.
3.  Sullivan's - They book good bands and the scene seems pretty cool,
although admittedly this place is the least familiar to me.

I hope this helps!

Cheers, 
Danny