The city's budget process takes place over many months and includes input, participation, and collaboration by many different stakeholders, such as:
City Manager & City Departments
The City of Austin contracts with a vendor (as it does every year) to conduct a statistically valid survey that measures city residents' priorities and how satisfied they are with city services.
In addition to measuring public opinion, the vendor also evaluates the results and provides the City Manager and Council with both the results and their analysis.
You can find the report here.