There has got to be a zillion bikes in Austin that would do the trick. You may have hit a slump in ads. Whenever I browse craigslist ads up here in Foat Wuth, sometimes I'll expand the search to Austin and always see something tempting.
Best buys are 1980s-'90s rigid fork mountain bikes. Check both the 26" and 700c types. My '92 Univega Via Carisma is a 700c MTB-lite, a predecessor to the later hybrid genre. Conventional diamond frame, would be brutal as a "mountain bike," but is terrific for all day rides on mixed terrain -- pavement to gravel. Over the years I've morphed it from the original flat bar as a MTB-lite, to a 2" riser bar with slight backsweep, to its current and probable permanent form with albatross swept bars as a do-it-all bike.
But check this forum's threads for the frequent "What's your favorite... etc." lists of the many brands and models that would be suitable for conversion projects.
You should see a ton of Treks, from entry level to mid-price chromoly or mostly chromoly bikes with some high tensile steel bits (forks). Nothing wrong with hi-ten steel, it's just a bit heavier but perfectly comfy to ride. My first serious bike was a 1976 Motobecane Mirage, all hi-ten steel. I rode the heck out of that thing, from 20 mile daily round trip commutes to 100-250 mile weekend group rides. I even raced a few criterium on it in beginner and intermediate categories, and managed to keep up as long as I drafted carefully.
BTW, the 1970s Motobecanes are good too but will need a few slightly different tools and bits and pieces. It's easier to find tools and bits for American made Treks or US market bikes. The French, Italian and other vintage bikes are lovely but more of an investment in money and love.