Don't know if you're much for baseball, Pooch, but a Cubs or White Sox game might be worthwhile. The Cubs play in one of the oldest ballparks in major-league baseball. The White Sox's park is substantially newer, but not as "earthy." The food there is excellent, however.

Springfield also would be an interesting day trip. In addition to the other sites already mentioned, the new Abrahan Lincoln museum/library is a must-see, so I hear (I still haven't made it there myself, although I'm planning to).

Anyway, hope this info helps. BTW, Sydney is one of my favorite cities on earth.