The most traditional honky-tonk is the Broken Spoke:
https://www.brokenspokeaustintx.net/
Can't guarantee doghouse bass and lap steel is pretty rare, but pedal steel, Telecasters, hats, and boots are certain.
The Continental Club is great, if you can get in. It's really small. And it features a lot of music beyond country. I once saw jazz guitarist Bill Frisell do a solo show there. Here's the schedule:
The Continental Club
Down the street about 8 blocks or so is C-Boy's Heart & Soul, managed by same people who run CC. Last coupla times Dale Watson was in town, he played C-Boy's.
C-Boy's Heart & Soul
Also worth a mention is the Saxon Pub:
The Saxon Pub – Austin TX
The big thing about Gruene Hall is that it's just cool to hang out in a place that been a continuously-running dancehall since 1878.
It used to be that you could drift down 6th Street, hear the music pouring out of the open club doors, and decide where to go in. But 6th St. is not what it once was. It's now a lot of shot bars, the music variety isn't what it was, it's gotten more violent, and the locals now call it 'Dirty 6th'. But I haven't done a good pub crawl down 6th in years, so my information may be dated. Check out the Tears of Joy hot sauce shop on east 6th though. (Their website seems to have a problem.)
A block from CC is Guero's taco bar, excellent Interior-Mex:
Güero's Taco Bar | Austin's Best Mexican Food
Lots of good stuff on the menu, my faves are the beef alambres, the chicken achiote tacos, and the El Magnifico marg. (The El Presidente plate is so named because that's what Bill Clinton had.) They have an oak garden outside that also has good bands.
San Antonians claim to have the best Mexican restaurants in the world, better than in Mexico. That's a big claim, but I've never heard anyone even try to dispute it.
[EDIT] You might find this story interesting too:
Back in Austin, the Ameripolitan Awards Define a Musical Spirit
