You have certainly picked a beautiful location. You might want to try dividing your schedule into the different zones
A day in Florence - remember to plan you museums and reserve.
You are in a great position for a quick day trip to Arezzo & Cortona
You are close to Siena and Montalcino
Maybe one day over towards Pisa & Lucca, probably the furthest away from your home base but well worth the trip.
Of course you are in Chianti so maybe a down day where you enjoy the villa and locals; may I suggest a local farmer's market in the area. Get some fresh cheese, wine and fruit ... October will be ripe with grapes, maybe figs - schiacciata con uva, a traditional foccacia bread with grapes and the last crop of tomatoes. Imagine all the fun you can have with these ingredients at the villa.
If you are renting Sat to Sat then you might want to think of Rome on the front end of your trip because the Vatican is normally not open on Sundays and Mondays will have many museums closed but if you come in on a Wed or Thursday before you go to the villa you will be able to hit all the main sites.
Buon Viaggio