I have driven a couple of times. No big problems, of small ones. I'd recommend to autoroute down toward Sienna,and then turn east. It will take a lot longer than you can possibly believe.

The roads in Chianti country are really crooked and narrow. They are also full of bikers,hikers, and tour busses. I have never done the direct route, straight north and south.

Getting back into central Florence can be a problem. Seems only the locals are allowed. Also, every street seems to be one way, and they are switched in direction at frequent intervals. Unless you are going to an obvious landmark, finding your way is not trivial.