There are many sources of 2010 census data for Chicago and vicinity. The Census Bureau's FactFinder2 allows you to download census data and GIS boundary files. Social Explorer (premium edition) allows you to make simple maps with 2010 census data. There are also many Websites with pre-made maps, e.g., a Chicago Tribune map showing population change by census tract.
GIS, as always, allows you to "personalize" your maps: to focus on particular phenomena or regions, to combine data from several sources, and to color the map in any way you choose.
Here are some 2010 census maps made with GIS at the University of Chicago Map Collection. They are set up to be comparable to the maps on the Map Collection's Chicago 1990 census maps and Chicago 2000 census maps Web pages:
Change in population, 2000-2010 (see note). Many of the trends established in earlier decades continued. There was considerable growth both on the outer edge of the metropolitan area--and in the central city. Farmland was still being converted to residential use on the urban edge, while, close to the Loop, population boomed in areas once largely given over to offices, factories, warehouses, or railroad yards. The areas of greatest decline continued to be inner-city low-income areas. The removal of high-rise housing projects made for some especially dramatic population drops. But there was growth for the first time in decades in some low-income predominantly African-American neighborhoods like Woodlawn and Oakland, where a considerable amount of new housing has been built. Also new: there was population decline in several gentrifying areas on the Far North Side. The pattern was complex in the generally stable outer parts of Chicago and in the inner suburbs.
Change in distribution of population by "race" and Hispanic status, 2000-2010 (see note). There was continued rapid growth of white population in favored neighborhoods near the Loop and on the North Side--as well as in the outer suburbs. Many of the long-established predominantly white neighborhoods in the outer city and inner suburbs lost some white population. There was continued decline of African-American population in many (but not all) low-income predominantly African-American neighborhoods. It appears that African-Americans have been moving into many largely white suburbs throughout the Chicago area. There was not nearly as much growth in Hispanic population in predominantly Hispanic Chicago neighborhoods as in the previous decades. Asians, like white people, tended to move outward and toward the city center. Many of the older North Side neighborhoods with substantial numbers of Asians lost some Asian population.
Change in per capita income, 1999-2005/2009 (see note). The demise of the long form makes it impossible to produce the kinds of maps and statistical analyses presented on the 1990 and 2000 census Web pages. The American Community Survey (ACS) is a partial substitute. It provides lower-quality data for running five-year periods. Data for the 2008/2012 period centered on 2010 were unavailable when this page was first put together. The map shows changes in per capita income for the period from 1999 to 2005/2009. The figures have been corrected for inflation. The spatial pattern of income change is rather complicated. There has been a continuation of some of the trends of earlier decades. Many non-Lakefront North and Northwest Side neighborhoods continued to gentrify--but so did some South and West Side neighborhoods, like Bronzeville and the Near West Side. Long-established well-off neighborhoods typically held their own while certain blue collar neighborhoods lost ground.