A few current Chicago maps:
Downtown Chicago courtesy of Chicago CartoGraphics
Downtown Chicago pedway and cut-throughs
courtesy of Chicago CartoGraphics
Chicago area expressways and traffic report names
multilevel streets of downtown Chicago the complex levels and ramps of Illinois Center and Lake Shore East
2018 aerial photos for Cook County late spring (leaf-off) aerials better allow roads and structures to be seen
“paper” USGS topographic maps online choose Scanned Topos in upper right corner
Chicago bike map online bicycling facilities and routes shown on Chicago CartoGraphics base map
Chicago rapid transit map all routes, even the crowded Loop, integrated into a simplified map
Transit isochrones how far you can get by transit in a set amount of time
Home prices data from Trulia
Public art outdoor installations in the City of Chicago
Employment nationwide map of where jobs are located
City of Chicago 80-acre cadastral map viewer alternate search by PLSS section
Chicago neighborhood map A map of neighborhood boundaries is inherently problematic, for reasons described here. But if you're determined to have one, this 2008 PDF from the city seems as good as any.
“Populated Places” of Cook County The national database of map locations includes some parts of Chicago whose names are unfamiliar, even to natives.
Chicago street guide PDF showing all Chicago streets with house numbers (2600 N, etc.)