2 nights in Tuscany

You could head from Rome and take the Chiantigiana, ending up in Greve.

Just so I understand, you are planning this:

• Leave Rome. Be aware this will be at least an afternoon worth of trip. If you left very early, you could spend some time exploring on the way.
• Spend the night in Tuscany, either in or near Greve or Castellina
• Spend the day exploring Tuscany
• Spend the second night in Tuscany
• Drive to Pisa

Be aware when you say you want to spend a day exploring Tuscany, it is like saying you want to spend a day exploring New Hampshire. Tuscany covers about the same area. You may be able to squeeze in a visit to three villages in a day, but it will be pretty much drive by tourism. We spent 10 days in Tuscany and hardly scratched the surface. There was not enough time to see all we had planned to see.

Will this day be on your arrival day to Rome?
If not ok
If yes not a good idea to drive after I assume an overnight flight

Sorry for the confusion. I have updated the question with more information. We are spending 2 nights in Rome and will leave for Tuscany early morning of day 3.

Where are you departing from?
As for choosing one place in Tuscany--you could throw a dart. Hard to go wrong really.
Since it is only two nights, I would try to minimize driving, and you don't really want to stop with all your stuff in the trunk.

PeeBee-
Siena is not really a "small town" and is a pain to drive in/out of for any day trips, parking also an issue there so I would take that off the list. Lovely though it is- it's a good drive to Pisa from there as well (close to 2 hours). The Chianti region DougMac suggest is lovely as well but a bit too far for your drop in Pisa next am.
Assuming you need to be in Pisa to drop car /catch train in the am I would want to be closer to Pisa.

You could drive from Rome to Montepulciano - have lunch make sure your luggage is hidden! We loved our stay in Montepulciano and the town itself can be enjoyed in just a few hours. Park at the bottom- take bus to top of town - walk down.
From there head to Volterra.
We are visiting Volterra in Sept and I found this hotel- seems to be about the only place with easy parking for in/out day trips.
It is right on the wall.
http://www.hotelsanlino.net/en/

You can visit Volterra that evening, visit San Gimignana the next day and maybe somewhere else-
Then you are only an hour or so to Pisa for your drop off next day.

Since your trip is soon you may be limited by where you can find lodgings with parking.

Pienza is also a lovely "flat" hill town. This hotel has parking on site with easy access/walk to town.
https://www.sangregorioresidencehotel.it/en/

If you don't mind two 1 night stays you could stop in Montepulciano for lunch- stay in Pienza then-drive to Volterra for the 2nd night as above.

I like to use www.rome2rio.com to do quick research on driving times/routes. Or viamichelin.com

Others have already commented that 2 days is very short so I won't repeat it .. : )

My inclination might be to explore based on the old Frankish pilgrimage route from Northern Europe to Rome - it's what made the fortunes of Tuscan towns, particularly those based along the Valdelsa - think Siena, San Gimignano etc.

So you could leave Rome and head for Lake Bolsena - it's quite a magical place and the Church of Santa Cristina is worth a visit - it has catacombs! (if memory serves).

From Bolsena head up to Tuscany proper, driving north past Mont'Amiata, an old spent volcano. There is a town there called "Abbadia San Salvatore" which has a fantastic 9th-century crypt under the church - featured in Tarkovskji's beautiful film "Nostalghia" - all about Tuscany and Russian poets...

You could reach Pienza in a relaxed day's driving and maybe spend the night there- (sorry I don't know any hotels there).

The next day go to Siena - you can park in an underground car park here https://goo.gl/maps/89cKS6sEejVEQAh28

There's plenty to see in Siena - I wouldn't miss the re-discovered crypt of the Cathedral, the Lorenzetti fresco of the allegory of Good and Bad governments and the Pinacoteca. Then head north up the Elsa valley, past Monterriggioni, Colle val d'Elsa then to San Gimignano and Volterra, if possible (it's a bendy road to Volterra). From Volterra Pisa is an hour away...

I hope this helps, have a great time!