Haven't been by car but flew there for a long weekend with Ryanair a few years ago. There is a campsite in town, quite close to one of the stations in the west side of Pisa. From what I remember the traffic wasn't great. You might be able to park at the edge of town and get a bus in as these were pretty useful - the airport on the edge and on the suburban bus route (also has its own station).
Sorry not to have been of more help, but you might try http://groups.google.co.uk/group/rec.travel.europe?lnk=gschg to see if anyone knows there.
When we went in 3 years ago, on advise of a local, we went in very early, parked on the side of the street, paid in a parking meter, went up the tower etc. and got out before it got busy with tourists later in the day.
Went to Pisa two Sunday's ago, drove almost to the tower and parked free, no charge on Sunday's and lots of empty bays,on street parking.Got there around 10.30am and busy with tourists.
Drove to Pisa on July 27th last year arriving at about 10.30am. Nightmare trying to park. Found a carpark near tower which was not quite full and entered but all spaces tiny and impossible to get into with our people carrier ( 4 kid necessity). Finally sort of abandonned it in a far corner of the car park which had stopped admitting people by then. Airport parking sounds like a good idea. Or else arrive about 6am! Although Tower etc. were impressive, we thought the rest of Pisa was very dissapointing. Also had to queue for over 30mins in full sun to get tickets. Hope you have a better day!