While it's not overly close, you can jump on the South Shoreline train from the park entrance. It runs ~2hrs, costs ~$14 and takes about 1 hours and 35 minutes.

About an hour to the Navy Pier, but like others have said, traffic can make a big difference.

It's about an hour to downtown Chicago without traffic. But in this area traffic is a big variable. All of the roads between here and Chicago are subject to traffic jams.