If you want to see the Tuscan countryside and find some wine and good food then you would be better off staying on the southwestern side of Florence, which is closer to Pisa, rather than venture into the more mountainous region east of Florence where Greve is.

Certaldo area is a great base as it is right in the middle of an area exactly half way between Florence and Siena in which there are some lovely places to see like Certaldo Alto, San Gimignano, Colle di Val d'Elsa, Volterra and Monteriggioni. The train station in Certaldo has a free large parking lot behind it so you can easily go to Florence (to the north) and Siena to the south) by train without having to worry about parking.

There are loads of good, inexpensive places to eat local food and there are also many family-run wine producers in this area.