I would like to rent a car in Florence and drive and see Chianti for half a day as that's all I can squeeze in my schedule. Maybe leave Florence around noon and come back late evening. Is that possible?
I'd suggest heading south out of Florence on the SS222 or Chiantigiana road toward Greve in Chianti, there are several wineries right before Greve that you can visit without advance bookings and do wine tastings. You'll enjoy the views and landscape - keep heading to Panzano for more great views, then on to Castellina in Chianti. From Castellina there are two fabulous roads you can take with more views - the one toward Staggia or the one toward Poggibonsi, you won't regret taking either... you'll eventually end up at the Firenze-Siena roadway, that is the fastest road to take back up to Florence at the end of your evening. But if you have time, and are near Staggia, you could also get to Monteriggioni, maybe have your dinner there before heading back to Florence.
Just make sure you check what times the car rental places close by so you can decide where to return it to and enjoy your evening better ;-)