I don't know about the cab fare to Pisa, but you might want to consider taking the train - we did this in May and it was quite simple. The added advantage is that in walking from the Pisa train station to the area where the Leaning tower is, you will get to walk through the town of Pisa which is really lovely with lots of shopping and restaurants.
Purchase the shuttle that the ship provides into downtown Livorno ($4 each way per person). The shuttle drops you off at a square with a tourist bureau kiosk in Livorno. From there, walk through the covered archway on your right, cross the main street to the bus stop and I think you catch the bus #100 to the train station (check the number with the ship) (buy a bus ticket from the tabacco shop right near the bus stop) . At the train station buy your ticket to Pisa - the trip is about 15 minutes through lovely countryside. I think the fare was less than 2 Euro.
Outside the Pisa train station is a billboard map showing the way to the Leaning Tower, it is basically straight ahead with a slight turn to the left after about a 15 minute walk through town.