The central shopping area is centered around the Corso Italia, between the railway station and the Ponte di Mezzo the central bridge and also in the Via Borgo Stretto, north of the bridge. However, many specialized shops are sprinkled around the city.
The area around the leaning tower is geared toward tourists: There are lots of small souvenir kiosks, stands and "flying merchants", selling all kinds of souvenirs from small statues to hour-glasses - of course the general motif is the leaning tower.
Beware: it is an offense to buy from one of the "flying merchant" that sell fake replicas. They are very persuasive and if you buy anything you must haggle – they'll drop their prices significantly.
Every two weeks there is a bazaar with quite cheap books, records and old household items.
And don't forget to try some of Pisa's famous biscotti biscuits or cookies. Bakeries all through town will sell multiple varieties, for a low price.
For the budget option, if coming from the Airport, there is a Coop supermarket on the left, on Via Pasquale Pardi.