Ciao Annalisa, I have to write back in English so that more people can find this information useful.
Your plan to organize a few days in Tuscany without renting a car for a large group is not too hard to do. I think it all depends on WHEN you would like to come, as in the summer there are for sure more people around and therefore you need to plan further time ahead.
Also, since you arrive in Florence but don't want to spend time in Florence, I would suggest planning to already head out from Florence as soon as you arrive. You can either: plan for private transport just the first day when you land to take you out into the countryside, or take a bus from near the airport to a nearby town or take the tram into SMN train station and then from there catch a train to where you want to go.
Depending on WHEN you're coming, I would suggest different locations. In the summer, you could head to somewhere near Pistoia and head into the mountains for trekking, or you could also head into Mugello and do trekking from there.
I would NOT suggest Chianti, as tree cover is more limited and summer can be quite hot for walking.
If you're coming in fall or spring, then Chianti would be a top recommendation.
If you let me know more details on when you were planning the trip, I hope I can offer some more ideas.
