George R.
Yelp
Jackson Park is one of the most peaceful and beautiful places in Chicago for an extended stroll. The real attraction, even more so than the giant golden statue, the hidden Japanese garden, and that bridge where the Blues Brothers drove the hated Illinois Nazis into the water, is the lagoon itself--simply beautiful. The last time I was there, I surprised a Great White Heron (no kidding) which was perched behind a rock in the Osaka Garden, who promptly spread his wings and took off over the lagoon.
Back to the sights though. The Osaka Garden is on the Wooded Isle, and is really easy to find. Stick to the right when heading south from the Museum of Science and Industry, or just take either path north from the 63rd St lot to get there--it's well signed. For a beautifully set, hidden Japanese garden on the South Side of Chicago, it can actually be a bit underwhelming. Where's Mayor Daley and his extravagant plans when you need him? The small pagoda there long ago used to be a tea house, and it would be incredible if the city would reopen that. The lagoon views are wonderful, though, and the arched bridge will delight kids if you have them.
The Statue of the Republic, unfortunately, is best seen by car, as there aren't any nice paths leading towards it. To get to it, take 63rd St east from Cornell and loop right around it. Make a point of seeing it, though, it's very impressive.
The infamous Nazi rally bridge isn't so exciting (again, but for the beautiful lagoon views), but you can find it on the east side of the lagoon by the yacht harbor. It leads south from the museum towards the tennis courts.
Less known than the above attractions are the bird watching trails. Heading southeast from the museum towards the Nazi bridge, you can get on a difficult to see trail on your right, which takes you through some woods to Bobolink Meadow right alongside the east bank of the lagoon. I didn't see any interesting birds, but I wasn't looking for them--the views were lovely.
There is always parking available in a lot off of 63rd St between Cornell and the Statue of the Republic, and the paths there both lead straight to the Wooded Isle. By the way, why is Yelp's map here showing the Indiana Dunes?!