I was asked in class this week for assistance in finding the current location in Chicago of a street address from the 1890s. Chicago did not come up with its current numbering grid for streets until about 1909-1911. Prior to that there was a hodge-podge. In the standardization all north-south numbers were measured from Madison and east-west numbers were measurd from State Street. In the process, many streets even changed names. During this process your ancestors may have appeared to move but really stayed in the same location.
Http://ChicagoAncestors.org is a wonderful site for those researching Chicago that was created by the Newberry Library--a privately funded library that is one of the best locations for researching Chicago area ancestors. From the home page one can enter a street address and it's location will be highlighted on a city map. From the TOOLS tab it provides a gateway to many free digital resources including historical maps, selected city directories and much, much more. Included are two downloadable documents about the street renumbering. Also, try clicking on the city map on the homepage. You can then explore the neighborhood in which you have landed. If you have Chicago ancestors, check it out and explore the various links provided.
This is a great site for searching online and for planning a Chicago research trip.