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Pisa is about 15 miles away but Florence is 60miles. Both can be done by train if you want or by ships coach. You would need a full day for Florenc.
We did both by car last year with Italian friends (driving like Italians). Livorno to Pisa in 30 minutes, 1 hour in Pisa (Leaning Tower), Pisa to Florence in 1 hour, 5 hours in Florence (lunch and cathedrals including top of San Lorenzo), 1 hour to Livorno.
You can do both in a day by train. Livorno Centrale to Florence (Firenze SMN) is about 1 hour 22 minutes. The 08:11 will get you there by 09:33. Florence to Pisa can be done in just over an hour - the 13:27 arrives in Pisa at 14:31. Pisa to Livorno is only 15 minutes and the trains run every 30 minutes or less. I realise that 4 hours in Florence won't do it justice, but I reckon it's worth a shot as a "first impression" visit. Visit www.railkey.com/cart/RailbestEuropeanSchedules.asp for more details on train times.