Good story by Teddy. Jackson Park, of course, is the site of Chicago's original muni, 9 holes in 1899, but that course is long gone. The first tee was at the current back door of the Museum of Science and Industry, with the shot over a lagoon. Tough opener! It then went to the current Bob o link Meadow and to Wooded Island (see the Google Maps view Terry Lavin provided).
None of that course exists today. The current 18 is, as Tom Bascanyi mentioned, on the edge of the city, and effectively intertwined with it. Before the U.S. Open was played at Bethpage Black, I wrote a column proposing a real public U.S. Open should be played at Jackson Park, as is, complete with ambulance and police sirens and all the roar of the city going on, in then-typical Jax conditions, with long fairway grass and take your chances greens. (They were beginning to improve under Kemper's management at the time.)
South Shore, on the other hand, is an original Tom Bendelow, of which there are few left. The original greens of 1905-06 came from Washington Park Golf Club when it (dating to 1896), and the original race track, closed at that time. I'd hate to see that gem torn up.