Pisa is a university town and the best food is found accordingly: cheap trattorias around Piazza delle Vettovaglie, a couple of more serious places in the old town, and one or two destination restaurants. Avoid anything within three blocks of the Leaning Tower, which is uniformly mediocre and overpriced.
Local specialities are Tuscan with a few Pisan quirks: cecìna (a chickpea flour pancake, eaten as street food), bordatino (a chickpea and kale soup), and ceci e baccalà (chickpeas with salt cod). The Pisani like their chickpeas.