Italians are very traditional about being at home with their families at Christmas. I have no direct experience of Pisa, but used to find myself driving from the Swiss border to the centre of Italy on Christmas day regularly a few years ago. Most restaurants, except the motorway service stations were closed - and the roads were as empty as I've ever seen, especially in the afternoon 'ore di paste' or mealtime.

Try contacting the Pisa tourist office or the local hotel association:
http://www.pisa.turismo.toscana.it/

Tony Bowyer