Tuscany

Evenings in Siena are especially lovely, with many options for al fresco dining, and the Piazza del Campo, a bustling gathering spot, filled with locals and tourists alike. That's the main appeal of staying there. It also has many attractions worth seeing during the day.

Florence has more sights and is worth spending more time to see everything, and with only three nights, it doesn't give you much time to do much in the way of day trips to other towns, even if you are arriving very early on your first day and not departing until late on the fourth day.

There's no one clear answer to your question, but if I only had three nights, I'd stay in Florence and spend two full days in there, and then if possible stop somewhere on the way in and somewhere else on the way out.

I'll be in Florence in May next year. I've been before, and this time it is for 9 day. Out of that I'll take one day for Siena. Yes, Florence is thick with unmatched art and history. With so few days there, you may want to check what is open if a Monday is part of your schedule. (The Uffizi, Bargello, Pitti Palace, and Accademia all close Mondays.)

forget the day trips. just spend the time in Florence. enough to see there in three to 13 days. Or the same with Sienna, although I would pick Florence. Less is more

I suggest Lucca, Pistoia, Certaldo, Monteriggioni, Volterra, San Gimignano, Montaione, Montefioralle, Volpaia in Chianti. They are lovely cities and small villages, you will surely love them.
If you are a lover of hiking I suggest to walk along the Via Francigena for a while (a beautiful path is close to Villa Ciggiano, near Castelfalfi and Montaione). You can enjoy an horseback riding tour there, also, and a quad tour too.
Well, don't forget about Pisa and Siena!
Anyway, enjoy Tuscany!

I would suggest making your home base Florence since there is more to do there than Siena. You can easily make Siena full-day trip by taking the train.

I would also choose to stay in Florence for all the above reasons. Siena is nice, and if you did want a day trip, I think the bus is easier than the train. Have a nice trip.