Having lived in Heidelberg I strongly recommend that you allow yourself time to view the city. 

The old city is wonderful.  I recommend spending a couple of hours on the Hauptstrasse.  Be sure to visit the Schloss (castle).  I would walk the entire Hauptstrasse getting a warm pretzel at the university and at the east end have a nice view of the Schloss.  There is also a great bakery where you can get some very good Black Forest Cherry Cake.

 There are nice views of the Schloss from the 'arches' and from philosopher's way which is on the north side of the river.

 I have known many people who...