How to waste time on the drive between Florence and Siena

First thought would be:
Monteriggioni which is right on the route for you

Would be a shorter trip than San Gimingnano but still similar problems that like all of the hill towns in the area that you have to park down below the town and then walk into town and than same on way out. Eats up time and the other concern is the usual luggage and valuables in the car while you site see is never a great idea.

Another thought would be south of Siena there is the Crete Senesi which is a very pretty area for just driving around somewhat aimlessly and seeing the unique and beautiful landscape there. Between Siena and Asciano is what I would look at on a map.
https://www.discovertuscany.com/crete-senesi/exploring-crete-senesi-from-siena-to-asciano.html

Drive down the SR222. See Greve, 30 minute drive, then on to Panzano 10 min. visit Dario the butcher (great snacks, very entertaining) then if you have time Castellina 15 min., very cute hill town.

If you only have time for two, I'd do Panzano and Castellina.

Thank you!

You can also get easily “wasted” with gerri’s Itinerary.
Lots of wineries along the way.

Gabriel, realize that when you leave Florence and head south, you are going into the Chianti region, where as Roberto mentioned, you could easily get wasted on the numerous wineries along the way. If you are into history or just want to see something amazing, I would highly recommend the American cemetery that is 7 miles to the south of Firenze. If you have ever been too Arlington Cemetery, it is similar on a smaller scale, but deep within a magnificent valley lined with cypress trees and umbrella pines. We went from Cortona to Lucca and stopped there with a car full of luggage and had no problem at all. Another hidden treasure that is so overlooked and in the vicinity is the Vinci museum in the town of Vinci. Engineers from around the world have made structures from Leonardo's drawings and it is fabulous. The second time we were there, we were leaving the town and had to stop for a shepherd leading his sheep across the road. It was magic!

When we were at Monteriggione a few years ago, the parking lot (not a big one) was right opposite one of the gates to the town. It was a pleasure, and a short visit to walk the entire length of the (short) main street. It even happened to be a medieval festival day, that they have every year.

The OP failed to give the month of the trip. A parking lot that size could easily fill up quickly in July or August.

Edit: Unless you have special arrangements with your hotel, allow PLENTY of time to park and walk to the accommodation. The town runs a bus from the parking lots, it can be so far, and so UPHILL. I don't remember any enclosed garages, like they have at, say, Orvieto. But Siena is very big. I had a lot of trouble with my GPS telling me to drive straight through the ZTL instead of going around the perimeter. I suggest you collect actual coordinates of two or three parking lots.

Spent several hours in Montereggioni in 2016, it was absolutely worth it to stop. How often do you get the chance to climb up to and walk along a medieval wall? The town itself is very cute, albeit touristy. It’s only a few minutes off the highway.

Wherever you go you won't want to leave a car full of luggage overflowing into the back seat.

Couldn't you leave Florence later? Is there something magic about the 8am pickup?

You've gotten some great suggestions. I'll add two more.

Drive down to Radda. It's a lovely little walled town with a beautiful old church. You can see the entire town in an hour.

What I really suggest is to take the wine tour at Castillo di Verrazzano. The tour takes 1 1/2 hours and includes a tasting of their terrific wine. The winery is in a castle with parts going back to the 12th Century! It is perched on a high hillside and the views are spectacular.

Thank you all for the suggestions. This will be in early June. I had another option, which I emailed Roberto about. My initial concern was that I would have to collect the car and drive off with it immediately after signing the paperwork for it. I purposely chose an 8 am pick up time in order to avoid any potentially long wait. My second option is to ask if the rental car company can keep the car in the garage until closer to 11 am, which is check out time. Or I can just collect the car and park it myself in a garage on the same street as the rental car agency. Our apartment in Siena is outside of the walls. So at this point we'll have to figure out the plan based on the car situation the day of pick up. But I would love to take a quick stroll through these small towns. But I do worry about that luggage in the car.

But I would love to take a quick stroll through these small towns. But I do worry about that luggage in the car.

I wouldn't worry too much about the luggage in small towns, especially in Radda, Greve and at the winery. Make sure you don't leave anything visible in the car itself. Don't retrieve anything from the trunk when you park. In other words, take the same precautions you would take if you parked in the parking lot of your local mall.

Folks tend to want to share their horror stories on the internet at least as much as they like to share their positive experiences. I think we lose a sense of perspective. I was concerned when we took our trip to Tuscany because of all the things I'd read about break-ins, pickpockets, ZTL's, speed traps, etc., etc. They Tuscany we found was not nearly as scary a place as social media can make it out to be. We took normal precautions and had no problems. Yes, things can happen, but being savvy and using situational awareness can minimize the chance you'll be a victim.

Doug, it's likely that there will not be room in the trunk to fit all of our luggage. Who knows, maybe there will be. But in case it is small, I certainly can't leave the car parked somewhere with luggage sitting in the back seat.

This is how you do it. Unpack your suitcases and pour the contents in the car trunk (and even back seats if trunk is too small). Like in the photos below:
https://goo.gl/images/v8fD9V
https://goo.gl/images/3aM11M

The valuables of course will be with you while you walk the town, the rest stays in the car in the messiest way.
Stealing a lot of stuff unpacked from a suitcase is not as easy as stealing a whole suitcase. At most they’ll take away a shirt and a pair of sneakers.

Sorry I missed the part about having luggage in the back seat. How many of you are there? How many pieces of luggage will each of you have?

3 adults. Likely 2 full size bags and 3 carry ons (not including possible purchases we have made prior to renting the car).