The census is mandated by Article I, Section 2 of the US Constitution, and is the most comprehensive source of population demographic information. Because it attempts to capture information at a household level and purports to capture an accurate count of the number of people in the US, it can be used to apportion Congressional representation.

From 1940 through 2000 a subset of Americans received a long form which contained detailed socioeconomic questions, but after 2000 the American Community Survey (ACS) was developed, and eventually replaced the long form as a survey that could be used to provide data for estimates between decennial censuses.

You get the following from each:

Decennial Census - Comprehensive counts of total population, estimates of proportions of demographic groups, availability once a decade.
American Community Survey (ACS)- Sampling for smaller groups, tables with aggregated response data on household income, educational attainment, and employment status, yearly availability for areas of sufficient size.
Public-Use Microdata Sample (PUMS) - Same questions as ACS, but available as anonymized individual responses, yearly availability for areas of sufficient size, high uncertainty bounds for small geographic areas and small groups.

Shortcomings in the data

The census does a poor job of capturing data on the homeless, incarcerated populations, and on undocumented migrants. Unfortunately, these groups often bear the brunt of disparities.
The ACS doesn't permit accurate estimates of small population groups, such as the immigrant and refugee communities in many cities, which makes it difficult to plan where to provide services.
The data capture population-level counts, but do not provide an easy solution for measuring changes due to migration.

However, once you know which census product to use, and learn more about the limitations of the data they produce, there is much that you can say about disparities in your city.