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.
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Laboratory dedicated to the cradles of biochemistry and housed in the old walls of Schloss Hohentübingen, in its close proximity to the Ancient Culture Museum.
The old city centre full of crooked half-timbered houses, small alleys, cobblestone roadwork and some nice old churches.
Stadtmuseum
Hölderlinturm
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.
A small modern art museum on one of the hills.