For nightlife, there aren't many clubs or live music places in Pisa: the usual night in Pisa is having a dinner of pizza or a cheap kebab, having a beer in Borgo Stretto, or Piazza delle Vettovaglie or a pub in the surrounding areas, and having a walk in Piazza Garibaldi and Lungarni, where the "spallette" (the low brick walls around the river) are full of students.
Some alternative clubs (hard rock, alternative, funky) in the center are:
Ex-Wide
Borderline
Less alternative clubs are found at the seaside, about 8 km from Pisa, in Marina di Pisa and Tirrenia. For instance
Pappafico (a disco with house music and the like)
PIA (a disco/bar on the sea)
Sunset (mainly a aperitiv/happy hour/chill-out location on the sea)
Take a photo of yourself holding, leaning against, or "anthropologically appropriating" the leaning tower of Pisa.