Staying in a Villa in Greve, Italy

Lucky you!
Greve is in the wonderful Chianti area between Siena and Florence. They are all connected by the historic highway, the Chiantigiana. We have spent four extended trips in this area.
Rent cars for your stay there. Parking will be relatively easy to find in these small towns.
We have stayed in Castellina and Panzano, both interesting towns to explore. Look for pottery makers such as Rampini Pottery. We have bought quite a bit from them and they always shipped it to our home.
Take a day trip to Deruta, Umbria and visit Ubaldo Grazia pottery, from the 15th century. We have several beautiful pieces from there, safely shipped for us.
Drive to other towns in the area such as San Gimignano, have lunch. Make a day of it. We did this with our young grandchildren and they loved seeing the different towns.
Start googling Chianti region to get ideas of what to see and explore. Get a Chianti Classico road map and start planning. Each town has its own personality.
What attracted you to stay in this region of Tuscany?

You will need cars. Most towns have traffic restrictions in the historical core, usually inside the ancient city walls. Those areas are called Zona Traffico Limitato (Limited Traffic Zone) and the sign is a white circle with a red border. Read below:
http://www.grandvoyageitaly.com/piazza/the-truth-about-ztl-zones-avoiding-tickets-in-italy