Check out the local Austin chapter of the National Association of Residential Property Managers (NARPM).
NARPM Austin Chapter - The National Association of Residential Property Managers PM Site by HomeRentals.net
I wouldn't hire a property manager who isn't a member of NARPM. I don't manage properties in Round Rock but you'll find a roster of Property Managers listed at the NARPM site. I'd contact several, at least 3 to 5, and ask questions. Don't email blast the entire list, or most will ignore your inquiry.
I've been managing rental property in Austin since 1990, mostly single family homes, I've seen a lot of owners make a lot of mistakes with the property managers they hire (before they found us). It's a very, very difficult occupation to do well. Don't hire based on the lowest fees, that's a huge mistake. Don't hire someone who's only been managing homes in Austin for a couple of years. A bozo PM can cost you bigtime with their mistakes and incompetence.
There are plenty of really good property managers who've been doing it in Austin for 10+ years. Hire one of those.
Good luck.
Steve