livery question

I do believe there were liveries, though none come to mind by name. You could check Austin Public Library's history resources or the Texas State Library's or even the UT Map Collection for historic buildings.

I will say this from personal observation, some of the historic dwellings I've seen in town have carriage houses. That's to say an outbuilding where the residents stored a carriage and stabled their horses. A servant would've taken care of the animals. This may not have been an option for your saloon keepers.

Now, this question got my wheels turning in my fever-addled brain and I turned up this about an 1870s-era opera-house/livery stable (when they said opera, think "opry" as in "I'm goin' to the opry and get good'n drunk." ) on Congress Ave that is due to be demolished. I think this is just the thing you spoke of:

http://www.austinpost.org/austin-history/historic-building-isnt-wrecking-ball-19th-century-structure

I live in Austin and actually stroll Congress pretty regularly.

Edit: here's the article in the Statesman: http://www.statesman.com/news/news/local/19th-century-building-on-congress-avenue-likely-to/nRNBD/

From my own research most towns of any size had at least one livery stable where residents could board their horses for small fees. Of course in a gold rush town those fees were much higher.

There's a lovely 1873 map of Austin on the Wikipedia page, showing Long's Opera House on the corner of Ash & Congress. The corner of Pecan and Congress had the Iron Front saloon where Bob Olive shot it out with Cal Nutt over rustling in E Travis Co. It even shows the train arriving in town.

I'd have thought there was a livery in every street when horses were the norm. In my current work I have it across the street from the saloon, cared for by a stablemaster, but people tie their horses to the post in front of it too.