Ciao Lana,
Florence is a great base for heading out to explore most of Tuscany and I can suggest various places to visit. Here are some basic tips for
renting a car out of Florence.
But how many days total will you have? Because there are 2 things to consider if you're planning to keep the car in Florence:
1. where to keep in overnight? if you're staying in the center, a limited traffic zone, you still won't have a PARKING permit to park inside this area even if you can enter the ZTL without a permit after 7pm (or later depending on season).
2. how far into Tuscany do you want to go? because you can definitely do a day trip into Chianti and return to Florence on one day, but if you want to explore southern Tuscany (as I think you should), then it would be more convenient to stay overnight closer to where you want to be and not have to drive back to Florence to head back out the next morning.
But if you can't stay out of Florence since your days are limited, I'd suggest staying somewhere that offers parking so that you don't have to worry about the car when you do have it.
Some examples:
Palagetto B&B
Hotel Principe
Villa Antea
If you want to stay close to Florence, I'd suggest one day head into Chianti and see Greve in Chianti, Panzano in Chianti, Radda in Chianti and Castellina in Chianti... the drive from Florence down the SS222 through these small towns is very scenic. From Castellina drive to Poggibonsi, a great drive as well and from there you can catch the Firenze-Siena road to get back to Florence.
The next day you can head to Pisa and to Lucca, driving in the hills in between. If you still have time, you could also drive up to Barga... the road there will take you past the Ponte del Diavolo, or Devil's Bridge - definitely stop there as well

.
OR
on the second day, you can head back toward San Gimignano and Volterra. Both are still very doable from Florence in one day.
Hope this helps - if you have any other questions, do post!