While in Siena, what day trips my gut you suggest? By car? Or bus? Car $$$
We are staying close to Siena in August and this last April I stayed there as well. I had a car and if you look at the map Florence, Pisa and Lucca are super close. We are heading to Florence for the day in August/Sep ..I do not know about trains.
There are plenty of trains and buses from Siena to Montepulciano, Firenze, etc.
Download trenit app. This will given you a view of the possibilities by train.
Trains are very inexpensive and frequent. Pisa and Florence are close. Siena is one of my favorite cities in Italy. You will love it.
Karren
Definitely Florence! That is a very quick bus ride. You have to eat Gelato in Florence, btw! If you have time, you can do Pisa and Lucca. Pisa only requires a couple of hours at most. Lucca, you can spend a day. But you need a train, still it is fast.