Data.gov provides access to statistical information gathered by the U.S. Census Bureau. You can search for specific categories such as income or educational attainment, or for all variables pertaining to geographies such as San Antonio or Bexar County.
Enter a zip code to see market segments by neighborhood. ESRI classifies people according to custom psychographic labels. People who live near Trinity, e.g., are described as "Set to Impress," which includes a certain set of socioeconomic indicators and consumer behaviors.
Survey reports, demographic studies and data-driven analysis from the Pew Research Center, a nonpartisan think tank. Research areas include: US Politics and Policy; Journalism and Media; Internet and Tech; Science and Society; Religion and Public Life; Hispanic Trends; Global Attitudes and Trends; Social and Demographic Trends; and more.
Search Google for media kits (sometimes called press kits), which often include demographic information about a publication's readership. For example, here's the media kit for Popular Sciencewhich includes a profile of the magazine's readers.