Drive from Florence south towards Panzano and Siena

Someone will chime in with routing info, but my experience with wineries is that many expect you to have a reservation for a tour, if that is what you plan to do.

Routes to SR 222:
Route 1 below gets you to the very start of SR 222 basically starting in the district of Ponte a Ema.
Route 2 gets to SR 222, but going through Ferrone and Passo dei Pecorai, then connecting to the SR222 just after Strada in Chianti. You'd miss the very start of it (basically between Grassina and Strada, along the Ugolino Golf Course, but the route via Ferrone is also nice. Lots of pine forests on that one. I love that portion.
From the arrival points in the routes below, then you just continue toward the SR222 (Via Chiantigiana).

All the routes on Google Maps routes below avoid the ZTL.

The ZTL camera is on Lungarno Vespucci, just East of the Ponte Vespucci. If you take that route, make sure you turn right on the bridge and not go straight toward Piazza Ognissanti.
But you will see it. The ZTL entrances have this circular white and red sign. This is the photo of the overhead camera in that place near the Vespucci bridge. You can't possibly enter it without noticing all of that, unless you drive inebriated.

For the return you will be very far from the ZTL if you return at the airport. Since you plan your travel for Saturday, the airport is the only option for your return as the other locations close early.
The airport Rental Center is on via Palagio degli Spini. It's not the easiest to find. Maybe the best is to take the A1 toward Bologna and exit at Firenze Nord, then proceed on the A11 toward Firenze (Florence). At the end of the A11 you need to veer right onto via Palagio degli Spini.

Route 1

Route 2

I might add that the Florence airport had some extensive construction last September.
Even though I've returned there previously it still took 2 loops around(due to lane closesurs) to return our car.
Just allow yourself some time.

Roberto, that is just fantastic, I'll just copy this map and use it.

I think I will take the route that goes west first and loops around up to the north and goes east, so I end up at the beginning of SR222.
So I assume the yellow flags on the map represent ZTL cameras?

Also I wanted to ask one more question: once I'm on SR222 and exit to the wineries or other small towns, like Panzano etc, is there anything specific I need to know about parking or do they allow parking anywhere?
Regards,

Zoe, yes I will make reservation with some of them, but i'hve read that if there someone there, most don't mind.

Gerri: yes, hopefully either me or my buddy are sober enough after the many sips and spits to figure out the turnaround, but thanks for the info.

What yellow flags?
The orange and red portions are the live traffic data from Google.

The route 2 via Ferrone is easier to find. I usually would take no. 1, because my house was right there near viale Europa, but the portion between Strada and Ferrone is really gorgeous with the pine forests. The portion up to Grassina is very urban, you are basically inside Florence. It's only after the Sardelli Oil factory in Grassina that the nice drive starts. But I prefer the Via Chiantigiana del Ferrone. It must be because it brings back memories of taking girls in those forests (then the stupid Monster of Florence put a stop to that).

We used this advice from Dall'Uva Wines last spring and had a fine day.

SR222 is a two lane road. The wineries are just a pull off from it. You can travel its entire length using Google Street View

Oh, when I opened the routes you recommended on my Ipad, the resulting map has yellow flags all over the map; I thought they might be indicators for the ZTL camera.
I just opened the map on my laptop, and there are no flags. That was weird.

Now you got me thinking about route 2. If the scene is urban all the way down to Grassina, I may have to consider route 2.

I will check out the wineries available along both routes and decide which one to take. I would like to stop by a couple of wineries going south, and stop over Panzano for lunch.