The US National Atlas website offers dynamic, interactive thematic maps, multiple map generators for creating your own custom maps based on available government data, as well as raw data available for download by GIS professionals.
The University of Chicago Library hosts a page with a smattering of Chicago shapefiles for ward district maps of the 90s, police beats, census tracts, and community areas. Most of this, as noted on the page, has been superseded by the City's own GIS portal, but the community area data should still be good. No license is given although there is contact info for a curator.