You can base yourself the entire 6 days in Chianti and take day trips... or just 4 days, then return the car and base yourself in Florence.
You're arriving in Siena first and will be staying there as well? Or arriving in Florence, departing from Florence?
Otherwise I'd suggest doing it opposite: first Florence, then renting out of Florence and moving out to the countryside for the remainder of the days.
For lodgings - I'd suggest you take a look at http://www.tuscanyaccommodation.com to book directly with the owners and get the best rates. I suggest a B&B in Chianti, depending on your budget I'd suggest: