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The long wooden boats operated by punting using a large wooden pole are a traditional method of shipping in the area. Professional punters offer a tour of approximately one hour around the island in the middle of the Neckar river. If you are more adventurous, you might try yourself at punting. It's not as easy as some of the professional punters make it look.
The old city centre full of crooked half-timbered houses, small alleys, cobblestone roadwork and some nice old churches.
The river Neckar next to the city centre, on which the students go punting (similar to what they do in Oxford or Cambridge in summer time, occasionally with a barbecue and a crate of beer on board.
The Schloss, or castle, can be a fun place to wander around. Look at the intricately carved gate at the entrance. Skip most of the centre courtyard and head up the stairs on the back side of the courtyard. This leads to a beautiful garden/courtyard, with some beautiful views from atop the wall to the left. Alternatively, go through the tunnel on the backside of the main courtyard that will take you through the backside of the castle, a much more medieval and beautiful part of the Schloss. At certain times, there are archers shooting in the eastern moat (the "Hasengraben") of the castle. From back here there is a path that will take you along the wall of the castle and through the woods, ending up on Haaggasse very near the Marktplatz.
Hölderlinturm
Stadtmuseum
A small modern art museum on one of the hills.