A great beautiful city to stay is certainly the medieval Siena, known for its Palio horse race but being really more than that! Siena is my most beloved art town and one among the most suggestive in Italy!
Of course Siena is not between Florence and Greve, as it is south of the Chianti region, but I would really consider it as a possibility. Though a larger town, Siena has all the charm of a smaller village.
High on top of a hill, Siena is made unique by its Piazza del Campo, its Duomo, its views and many more attractions.
In alternative to Siena, you might consider spending your night in any of the small charming villages of Chianti.
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Enjoy your stay in Tuscany!