The metropolis four hours to the west of Ann Arbor. Drive I-94.
Or board the Wolverine Line at the Amtrak Station three times daily. It generally leaves Ann Arbor 8:23am, 12:48pm, and 6:11pm. The cost is $26 on weekdays and the trip is about five hours. But trains always run late -- don't trust (or count on) Amtrak's times.
Chicago is an interesting piece of Ann Arbor's regional identity, in that residents seem to visit there more frequently than the much closer Detroit. The Daily claims that 14% or so of Michigan graduates go to "Illinois". We all know what that means.