Family of 4 next June-Can we visit Sienna, San G, and Tower of Pisa in one day? Know this is whirlwind, but can it be done?

Yes, of course you can do it, you can drive as far as you want in one day. You can see the Leaning Tower in the middle of the night if you have to.

Do you want to just run in and out of these towns?

No, not in June which is peak travel time both for tourims and Italians themselves especially schoo groups. Even leaving Florence at dawn, you would be hard-pressed to get parked and get in and out of each of the towns listed before dark. Arrangemnts made to alleviate congestion in the centre of each neccesitate transport (or at minimum a good walk) in and out from lots. Skip one and from my perspective Pisa is the one to skip, though it is a shame...but there is always next time!

Tex, my recommendation would be to focus on Siena. On the way back you could have dinner in San G which is not that far. I have not been to Pisa, but from what I have read, it can be missed.

Enjoy Tuscany!

San G. and Sienna are close to a full day even in the off season. A problem is that they lay in a different direction than Pisa or Lucca, which is also close to a full day.

Pisa will have more tourist than Lucca, but you can see the Tower area in 2 hours, and then go to Lucca.

Personally, I was not that impressed with Sienna, but worth a trip anyway. I liked Pisa better, but its only good for a quick visit. San G. is nice, but can be seen in 1-1.5 hours, but it is out of the way and takes time to get to.

Taking the train will get you there faster than driving and you will not have to find parking. San G. is not on the rail, but can be reached by train and bus or bus from Florence.

If you are going Florence to Siena, you are beter off going by bus. No change necessary, and the Siena bus station is in the center of town, not outside the walls.

Years ago I copied from this forum advice from Italy expert Paulo on how to see San G and Siena in one day.
here is the abridged version, but check the current transport schedules:

“…San G. doesn't have a train station of its own. It's served by the train station at Poggibonsi and a bus or taxi to shuttle between both cities would be called for…There aren't direct buses from Florence to San G…
There are frequent buses both ways between Siena and San G… In this case, I would take an early (6:30am or 7:10am) SITA through bus from Florence to Siena (arriving at 8:00/8:40am; SITA bus station in Siena is across the square in front of S.M.Novella train station). After visiting some of Siena and lunch, I would find my way to San G. midafternoon by bus. After visiting and having an early dinner, I would get a taxi to Poggibonsi and a train from there back to Florence.”