one home base for 4 nights in Tuscany?

I would base in Pienza or Montepulciano
4 nights is not 5 days- it is 3 full days

Where and when are you getting the car, dropping the car?
You could visit SG and/ or Volterra on your way to Florence

Or plan to drop car in Siena and spend a night there before Florence

ETA
I see from your other post you are thinking of car from FCO?
Pienza and Montepulciano are both easy drive from FCO
You might start looking for accommodations with parking to see what your options are
Pienza is very easy to drive in/out and there are several hotels just outside walls with parking

Note-Cortona is closer to Montepuciano/Pienza not SG/Volterra
Other towns to visit from Pienza area-San Quirico, Montalcino, Monticchiello, Bagno Vignoni, Arezzo

All the towns you plan on visiting are extremely popular with tourists. If you want to experience a quieter, more authentic Italian village or town, try picking a place you have never heard of. Since you will have a car, that gives you a lot of options. But you also don’t want to spend all your time driving, so I would suggest keeping your day trips to a smaller area.

With just 4 nights, I would stick to one base. Moving eats up time. Of the towns you listed, Pienza and Volterra were my favorites. I found San G. kind of dull. We were able to pick up a tour of the papal palace in Pienza through the TI office. I have no idea if that tour is still available, but it was terrific.
One thing to be careful about. Roads in Tuscany can be narrow and winding. A 25 mile distance may take an hour to cover.

I would suggest basing in Pienza for the simple reason that it's probably the most difficult place (of the towns on your list) to find parking when visiting during the day - although it can be somewhat tough finding parking in Cortona too.

Pienza is really nice in the morning before it gets busy with day visitors, and especially in the evening after they all leave. There are many nice towns to visit within an easy drive from Pienza, east or west on SS146, or south on SR2.

We did Tuscany and stayed in Siena as a base.

I would choose one base. We stayed in Siena last May, and we really enjoyed our stay here. From Siena, you can visit San Gimingnano, Volterra, Pienza, Montepulciano and Monteriggio. Since you are heading to Florence afterwards, which is what we did, you could easily visit Monteriggio on the way to Florence.

We loved Siena! The campo is amazing! The Duomo is stunning! We followed Rick's walking tour of Siena. Every meal we had was delicious. We stayed at Hotel Palazzo Ravizza, and they do have parking. The views from our room and their terrace, where you can have drinks, are gorgeous.

I also think Pienza would be a nice place to stay. We couldn't find parking in Montepulciano so we weren't able to visit, but it looks busier and larger than Siena and Pienza. I might prefer Siena, though, because you would have more dining options in Siena than Pienza.

Montepulciano is much much smaller than Siena by about 40,000

i don't think we will base in or near Siena since we've visited there before and want to focus our attention further south this time. I'm thinking an agritourismo in the Pienza/Montepulciano area would be a good base to see much of the area/towns? Any thoughts on a specific accommodation?

https://www.agriturismolabruciata.it/en/
This is 3km from Montepulciano and super close to Pienza. We spent the best week here enjoying her villas and exploring the Val d’Orcia. She even prepares dinner for you on your arrival night. Breakfast is all local from her farm and prepared by Lara and her mother. I would love to stay here again!

We are looking for a similar stay too! Did you settle on a town? We are driving from Cinque Terre, stopping in SG and then headed south for 3 full days before driving to Florence. Hoping for somewhere with a beautiful view, good hospitality and on the romantic side vs family friendly.