Ciao Cynthia,
4 days are going to pass really quickly, but you can certainly do most of what you're already planning.
Since you really should visit Pisa, your first half day afternoon sounds like the perfect time to do it.
Pisa is well connected with Florence by train so you have two options - go first to Florence by train, and then rent the car as you don't need at all in Florence but will need it for the rest of Tuscany OR rent the car right away and then return it on your last day spent in Florence. You can then once again reach Pisa airport easily by train (or bus).
Another day can be spent in Chianti - if you take the Via Chiantigiana from Florence into Chianti, between Greve, Panzano, Radda and Castellina you'll find many wineries along the road with signs that invite you for wine tastings. Many have shops along the road or just off it on the estate.
The last day you could spent it in Siena. It is very different from Pisa and Florence, so this will give you a chance to see a little bit of everything that makes Tuscany so special. My advice is to move each day to the area you'll be in, to avoid driving so much back and forth. While none of the cities are too far from each other (Pisa to Florence is about 30-40 min while Florence to Siena is about 50-60 min), it is still an hour or two spent going all over the area. So you can spend the first night in Pisa, the second night in Florence, rent the car and then spend the third and fourth night in Chianti (for example, at
Palazzo Malaspina - take a look at other
accommodations in Chianti) so that you are close to Siena and can actually also include a visit to San Gimignano on the way back from Chianti to Pisa.
Does the itinerary make sense? Feel free to ask more questions if you have them!
