The National Statistical Agencies section in Sócrates Reyes' research guide, Statistics and Data for Latin America, lists links to online data that may include city-level data. Note that you can change the interface language to English on some sites if you don't read the default language.
See, for example,
Argentina: 2010 Census/Censo 2010. Begin by selecting Provincial under Alcance.
Brazil: Instituto Brasileiro de Geografia e Estatística (IBGE): 2010 census. City-level data available here: Ciudades@.
Mexico: Instituto Nacional de Estadística, Geografía e Informática (INEGI). Choose the state from the dropdown menu by the map, México en cifras/Mexico in figures. Then choose the Municipo/Municipality on the underlying page.
The comprehensive Country Statistical Yearbooks research guide from the University of Wisconsin-Madison Library links to online national statistical agencies. Some of these sites include data for cities in that country; you will have to explore the site to uncover the city data when it is available.