Visit the University
Visit the University, drink a coffee in Cartola (it's the cafe at Praca da Republica).
Have a meal somewhere in those little restaurants downtown.
Go to http://195.23.44.46/index_html?lingua=i to find an interative map where you can locate interesting places. Listening to Fado de Coimbra (specially on the first night of Queima das Fitas; first thursday of May).

Coimbra - Portugal
Pedro and Inês - by the Olga Roriz dance company
Coimbra (Portugal)
Pátio da Inquisição (Coimbra, Portugal)