Ciao!
Are you planning to use Florence as your base and just rent the car for a day to drive out and roam, returning to Florence by the end of the day?
Or will you spend also be spending a few days out in the countryside?
I vote for the second option, as it will give you a chance to drive further away from Florence and see a wider variety in landscapes, particularly those "classic Tuscan" rolling hilltops with cypresses along the roads (more common in the southern area of Val d'Orcia which is further away).
In any case, I suggest taking a roaming circular drive around Chianti as a first suggestion: take the SS222 down to Greve, down to Panzano, then on to Castellina. From there head west to Poggibonsi or to Monteriggioni -- those hills with vineyards are gorgeous. From Poggibonsi, make your way to San Gimignano. From there, head to Certaldo by way of Gambassi Terme.
I think once you do that, you will want to spend more time out of Florence, particularly Jill so that she can be out in the countryside in mornings and evenings when the light is better ;-). What time of the year are you coming?