Having grown up in and lived most of my life in the Chicago area, the rationality of the grid system is rather nice. If you know your “hunnerts”¹ you can find anything. Every 8 hunnerts is a mile except for the first three miles south of Madison where the streets are numbered.² A handful of suburbs use numbered streets for north-south streets (Cicero and Elmwood Park—maybe others but those are the ones I know). In the city, there was a plan to have north-south streets named with the first letter indicating the distance in miles from the Indiana border, but it only really starts with “K-town”⁴ between Pulaski and Cicero Avenues and while most streets follow the pattern, it’s not universal.
Some distant suburbs (Du Page County and beyond) use a numbering scheme of xxWyyy where the xx is the number of miles west of State Street (the 0 in the cartesian grid of Chicago) and the yyy is the location within that mile. I don’t think they do anything similar for North-South coordinates though.
The diagonal streets in Chicago largely follow the routes of early non-grid roads of the city (many of which were plank roads run as toll-collecting businesses and followed paths used by the native American tribes living in the area before European settlement.
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1. Hunnerts (from hundreds) being Chicago-speak for the location on a grid. E.g., Chicago Avenue is 800 (eight hunnert) north and Western is 2400 (24 hunnert) west.
2. This is a consequence of history. All the missing numbers (Roosevelt at 12 hunnert south is the first mile, Cermak/22nd street at 22 hunnert south is the second and 31st street at 31 hunnert south the third) do exist,³ but the streets were named and numbered before the replatting established the modern hunnert system.
3. There might not be some of the hunnerts in that first mile—the numbered streets only start after Roosevelt.
4. Not to be confused with Los Angeles’s K-town where the K stands for Korea.