I love stuff like this. According to the Baseball Toaster the geographic center of the American League Central (our beloved home after all) is none other than Addison, Illinois.
http://humbug.baseballtoaster.com/archives/314423.html
The precise location in Addison appears to be someone's backyard in the middle of a residential area. Somewhere around N. Lombard street off IH-355. Of course, this is Cubs' country.
Math always surprises ya, and I'm surprised that the division's center is that far north, but then again, we are the southmost team in the division.
And I'm sure you remember the Royals Review feature on the bitter Royals-Rockies rivalry which has Gove, Kansas as its epicenter.
http://www.royalsreview.com/story/2005/6/25/22247/3286
Royals-Rockies: This Means War!
Of course, according to Cardinals fans, the middle-point of the Royals-Cards rivalry is somewhere outside the KC city-limits, because of course everyone else supports those lovable Best-Baseball city sepia toned uber-fans.