When I went through college orientation, the one thing I thought would be the most helpful, as an introduction to Chicago, would have been to be quizzed on the numbers of the major streets; once you have that down, the magic of the grid is that you can get almost anywhere and have a sense of how long it will take. I still don't have it down, because I have a terrible memory, and am constantly having to ask people "sorry, what number is Belmont/Irving Park/Kedzie/etc." I wonder if flash cards would sell.
It's a game: you get the name of a neighborhood, you have to click on where the neighborhood is. (There are other cities, but we invented the city-of-neighborhoods thing.) It took me about 10 minutes to place all 92 neighborhoods; there are more, obviously, but it's simplified for scale. You will probably do better, as I get performance anxiety, and totally forgot where Galewood is.
(Perhaps superior to Click that Hood, but still offline, is a game I heard about from Eric Zorn at a recent TribCo event: Median-Income Darts, apparently invented in an old Trib bureau and clearly the sort of thing that comes from the minds of people who constantly have to look up data. You throw a dart at a map, and you get points based on the median income of the town/suburb/neighborhood. Actually sounds like a good learning tool, if you have to do a lot of on-the-fly sociology.)