Basemap (background map) from OpenStreetMap: Install the "QuickMapServices" plugin. In the toolbar, there will be a little globe with a "plus sign". (The tooltip will say "QuickMapService".) Click on that. In the pop-up menu, select "OSM" and then "OSM Standard".
Austin City Zoning Zones You will to click the "Export" button and select "GEOJSON".
Appraisal data from TCAD (Travis County Appraisal District). You can download appraisal data from the "2022 Appraisal Roll Export" link on this page. It contains data like the appraised value, size, state zoning code, number of structures, squarefootage, etc.. The data is fixed-width. The fields are described in the "Appraisal Export Layout" file.
City of Austin GIS Website No data. Just links to stuff.
Austin's Open Data on Locations sorted by popularity Open data include zoning cases, construction permits, business permits, police stations, pools, City-owned trees, etc.. Some specific ones are below.
Roads from USGS People use rivers and highways as reference points and you can download the highways here. The largest highways are "controlled-access highways".
Boundaries of Travis and Surrounding Counties There is also a map of All of Texas County Boundaries