Forget the taxi to Pisa. Take the train. In fact you can take the same train to Florence and stop at Pisa on the way. You may or may not need a taxi to the train (I don't recall), but European trains run on a very regular schedule.
I am the editor, but I also speculate, ask questions and play devil's advocate. I reserve the right to change my mind.
I studied in Florence for 5 weeks and have been to Italy numerous times and I totally agree with Paul - the trains are def. the way to travel when in Italy. Just beware of strikes which are frequent in Italy and can last up to a few days. Overall the trains are much cheaper, cleaner and probably faster and it gives you a great way to enjoy the gorgeous Tuscan countryside