Your first base could be Florence. If you plan to hire a car at Pisa airport, then you easily get to Florence via FI-PI-LI highway and find there your first accommodation. Have a look at
this page for a selection of self catering lodgings. I suggest you choose an accommodation with private or public parking situated close by.
There you'll find everything you may need at an easy walking distance and visit both Florence with its tourist attractions and Siena, situated at an hour driving distance.
I suggest you take also a drive to Chianti as well, its gentle hills are really worth your while!
Then you could move to Pisa (
here you'll find some suggestions for choosing your accommodation - Pisa, Livorno and Versilia offer many hotels instead of self catering accommodation, but I think it's the best location you may choose for seeing all the places you've planned to) and visit the city with its famous Miracles Square. From Pisa you easily get to beach resorts by car: Marina di Pisa, Vecchiano and Versilia (Viareggio, Lido di Camaoiore,......) are just a few locations situated at a very short dirving distance (less than half an hour).
I suggest you take a drive to Livorno also: sandy beaches are less than rocky ones, but they are all actually marvellous and some other famous sea locations - such as Vada, Donoratico, Rosignano Solvay and the Etruscan coast) are not so far away.