Ciao Paula and welcome to our forum!
What do you kids love to do? Do they love museums, art or history? Architecture?
You can plan to spend your days between outdoors and indoors so as to not get overloaded on any aspect, but why skip Florence - have you already been? It is definitely a must for anyone visting Italy but if you've been already, I can understand skipping it. In any case, once you decide where to head off to, try to balance out what you do at each place with things you want to see and do and what the kids want, so that you all have a good balance.
I would suggest staying
central in the region so that drives are not too long, the area between Siena and Florence is ideal for drives to Pisa, Lucca, Siena, San Gimignano, around Chianti and even further south into the Val d'Orcia.
The area itself is large so I'll make suggestions for places to stay across the area, take a look at these which work great for families:
Agriturismo Montalbino - closer to Florence
Agriturismo Vernianello - between Castellina and Poggibonsi
Podere Casanova - closer to Florence too
Agriturismo Incrociata - closer to Siena
Tenuta Quadrifoglio - between Florence and San Gimignano
You can also consider the area just a little bit south of Siena, particularly if you decide you don't need to be so close to Florence.
Podere Cunina - near Buonconvento
San Giovanni in Poggio - a bit further north of Buonconvento, closer to Siena
Take a look at the itineraries we have on here for ideas of what to see:
Itineraries in Tuscany - We have one for 5 days:
https://www.discovertuscany.com/itineraries-in-tuscany/five-days-in-tuscany.html