Aside from Hyde Park/Kenwood there are some interesting hidden-away neighborhoods on the S Side, like South Shore, Morgan Park, Beverly, Chicago Lawn (which was quite a suprise...big old victorian houses from an old railroad suburb that was swallowed up by the city...sort of a South Side version of Irving Park)...and more blue collar areas like South Chicago, Back of the Yards, Bridgeport, Hegewisch, and that Polish area off of Archer (Bubaks or Bobaks grocery..what a find that was!)......
...and those bouelevards extending north from Washington Park...some interesting romanesque revival townhouses and villas there.
My experience w. Chicago while living there was nearly all on the Northwest side with some on the pre-gentrification N Side...with very little to no connection w. the South Side. I return at least twice a year now on visits and have been exploring the South Side more, and it is like a whole new city for me.