The databases linked on this page are "best bets" for the kind of research on 1950s Chicago you're doing this term. Similar resources are available for lots of other times and places-- we have databases of medieval art and access to the current New York Times, for example. But these sources will be helpful starting points for the current semester's work.
Visual and oral sources can provide primary source evidence. For example, try searching ArtStor for pictures of Chicago, and limiting the date range to the 1940s-1960s. History Makers provides first hand accounts and interviews with prominent African American figures.
Historical newspapers and periodicals are great resources for finding out about details of a historical period that might not make it into the history books. What restaurants were opening or attracting attention? How did people at the time respond to historic events like the passing of the Fair Housing Act? How were prices fluctuating? Even the weather report!
When pursuing primary source research, it's often helpful to go to look at digital collections at libraries from the area you're researching, as they will often have the most substantial collections on their area. For Milwaukee research (and a few Chicago items), you might try UWM's Digital Collections. The collections below might be especially helpful for Chicago history research.