What about Siena, San Gimignano, Casole d'Elsa?
Siena of course is not a village, but it is not exactly a big city as well, it is more like a kind of medium town with a great, glorious history. Beautiful to visit and to live in honestly, also if in this time of the year it probably tends to be quite crowded.
Anyway you'll find plenty of agriturismo (farmhouses) that are situated outside of the city, and where you can enjoy some quietness.
Of course, there are trains and buses going from Florence to Siena a few times a day.
You can get to San Gimignano and Casole d'Elsa via Poggibonsi train station, a medium-sized town situated between Siena and Florence. I would have recommended also Poggibonsi, though it is not as beautiful as the others, yet more authentic, but I'm not sure you'll find a place to stay outside from the town reachable in 1.5 miles walk. In Poggibonsi anyway, you can catch buses (and taxis) going to other villages nearby.
Anyways, San Gimignano is just a few km away from Poggibonsi, and there are buses taking you there during the day. It is beautiful, but there are many tourists over there right now. So, also in this case I suggest you to get an agriturismo out of town and then walk there. There are plenty of them.
Casole d'Elsa is harder to reach by public means, but still there should be some bus going there from Poggibonsi. Casole is situated in a very panoramic position, is very quiet and the people living there are a cohesive community.
Hope this was helpful somehow...