Pisa is a city tourists visit to see the leaning tower, but Pisa is a very pleasant University town along the Arno in Tuscany. Pisa falls under the classification of a Mediterranean climate, like most of Central and Southern Italy.
Pisa's weather is influenced by its proximity to the sea. In late fall the precipitation starts, as you can see from the historic climate charts below.
Spring is a fine time to visit Pisa. The Regatta della Antiche Repubbliche Marinare, or regatta of the old Maritime Republics, is held in Late may or early June, usually in fine weather. Eight man crews race against each other along the River Arno; don't miss the medieval parade along the banks of the river. (See Pictures from the 54th Regatta)
The rest of Pisa's big festivals are held in June, the Festa di San Ranieri, when the Arno is adorned with torches, occurs on June 16th, and the next day there is the Regatta di San Ranieri.
The off season, April-June and September and October, offer the best weather and fewer crowds at the leaning tower. Expect days of rain in October and November and winter is very damp.
Sure, you're going to get off the train at Pisa Centrale and run to the Leaning Tower as if that were the only attraction in the city. You'd be wrong, but we'll aid and abet your efforts with a video: Getting from Pisa Train Station to the Leaning Tower in a Hurry.
We have some specific recommendations for eating and staying: Pisa: Where to Eat, Where to Stay