The Lone Star Court in The Domain that is about a 35 minute drive from Villa Antonia. The Domain has ample food and entertainment within walking distance, and is also a short drive to many of the sites and things to do around Austin.
If you are interested in being closer to the Villa Antonia, there are many rental options (e.g. Airbnb, Vrbo) on the north or east side of Lake Travis that are within a 15 minute drive of the venue. These rentals also can offer more scenic views or be closer to nature due to the proximity to Lake Travis.