there are quite a few well organized tours that you can take part in where you will see lots of both Chianti and Siena - just have a look at these tours
However, if you are the kind of person who likes a bit of adventure - this area is easy to navigate and you can certainly do it on your own, at your own pace. Some of my favorite places to stop at while driving from Florence to Siena include:
The first place is barely outside of Florence - not very well known and most probably requires an appointment. But in my opinion well worth (if not for the wines ha!) for the views and to experience a Medicea villa. http://www.medicivilla.com/
Definitely the tips are going to be useful for us! @ this point we are renting a car in Siena then going all the way up to San Gimignano - maybe Volterra as well - in the morning then in the afternoon we are planning to visit 2 or 3 wineries @ Chianti.
Well, we are going to have 3 days in Siena then we are trying to figure out how to spend 3 days in Tuscany! One of the 3 days we would like to go to Assissi then Orvieto as well! Any suggestions for these places?
If I had to choose between Assisi and Orvieto (because it is just not possible to do both in one day) I would go for Orvieto. Assisi is great, and you can combine it with Perugia and also a stop at Lake Trasimeno but my preference is towards the south and Orvieto....if you really wanted to and had some extra time you could try and combine it with a little park Dunarobba (http://www.paleonature.org/en/famous-locations/165-the-dunarobba-fossil-forest)
I loved walking around this town - it is loaded with great little restaurants and of course ... the wine!
I strongly encourage you to check out the tour of the caves under the city - absolutely fascinating.