Personally, if you rent a car, you should use it to visit places where a car is more efficient than public transportation. Therefore a car should be used to visit any of the following:
Chianti Hills, San Gimignano, Certaldo, Volterra, Monteriggioni, Pienza, Montepulciano, Montalcino, Val D'Orcia (San Quirico, Buonconvento) and many other places in the area. For example, Volterra can be easily done together with San Gimignano (both IMO are must see towns) and maybe even Monteriggioni (another must see fortified village).
Siena is a must do town and in the general area where the above towns are located, but the car is of no use there, so maybe you could visit it from Florence without a car and save yourself a car rental day (it's 70 min away by bus from Florence). Siena can easily take several hours to visit. If you do it by car, take advantage of the car and drive through the Chianti Road (SR 222).
Orvieto and Civita are kind of far from Florence and the rest of the places you want to visit in Tuscany and would be best done from Rome (are you in Rome at all during your trip?) or maybe on route between Rome and Florence. Unless you are going to Rome in this trip, I would ditch both because it's a detour from the rest.
Lucca and Pisa are next to each other and can be done on the same day. Neither one is a hill town (both are flat)
Lucca is a pretty fortiified town and I think it deserves most of the day if you visit Lucca and Pisa together.
Pisa is a one trick town with only one square to see (the Field of Miracles) which contains leaning tower, cathedral, baptistery, cemetery. Two hours are enough. In fact, since you are going to the Cinque Terre later from Florence, and you will need to change trains in Pisa, I would visit Pisa in between train changes. Just deposit your luggage at the station luggage storage, visit Pisa, then retrieve your luggage and proceed to the Cinque Terre.
Another alternative is not to return the car in Florence, rather go from the Tuscan towns, directly to Lucca/Pisa by car, then from there proceed by car to La Spezia (next to Cinque Terre) where you can return the car. Then from La Spezia take the train to the Cinque Terre (10-15 min). This is actually what I would do in your shoes.
So this is my proposed itinerary:
day 1: rent a car in Florence, drive the Chianti Hills all the way to Siena, visit Siena.
day 2: Val D'Orcia area (Pienza, Montepulciano, Montalcino, Buonconvento)
day 3: Monteriggioni, San Gimignano, Volterra
day 4: Pisa/Lucca, return car at La Spezia (Cinque Terre)
Or spread more if you have any extra day.