Best Day Trip from Siena with a car

Run over to San Gimignano before the tour buses show up. Then go down to Volterra for lunch.
Make sure you have a place to park that rental car. Siena is pretty congested with apartment complexes and with the city up on the hill.

The most popular is the drive on the SR222, the Chiantigiana road.

Start in Greve in Chianti, then Panzano, and on to either Radda or Castellina.

If you must stay in Siena there are many options, including the ones offered above. I prefer the landscape and villages a little further south. I'd start off with a visit of Monte Oliveto for coffee (if the restaurant is open early) and the abbey: it's in a lovely location. A bit further south are the little visited San Quirico, delightful Pienza, and the well visited Montepulciano. They are all worth it if you have the time but don't rush. I once got lost driving around in the area and it was out of this world.

Every single recommendation above is great.

We did Volterra in the afternoon and stayed outside the walls to witness one of the prettiest sunsets I've ever seen. The town was glowing!

We also visited Monte Oliveto, but went mid-afternoon, had dinner, then returned for Vespers.

Grazie!!!!

The advice of David is exactly on point. I recommend that you follow it.