Recommend Florence and Chianti as your two bases
Ciao Christina,
I think the best way to start is from a flexible itinerary you'd like to follow for your week, that way you can decide what the best areas to stay in are and from which to do your day trips and then the rest comes after that.
Is this your first time in Tuscany? If so, I'd suggest staying a few days in Florence (at least 2 nights), a definite must-see! That allows you to see the main sights in the city without having to drive back and forth from wherever you are..... and then move on to somewhere in the Tuscan countryside from which you can then focus on day trips near to where you are staying.
In Florence, I'd recommend you stay in the
historical center. This way you and your parents are in the heart of the city, walking distance to all of the main sights in addition to having a place nearby to head back to if they (and you too of course!

) need a bit of a rest before continuing sightseeing or heading out to dinner.
Rent a car only once you're done with Florence to head out to the countryside. You don't need a car at all in Florence, everything is walking distance and for anything a little further away, you can catch a bus.
Use the search box on
this page to see various rates across main car rental companies.
With the car, you can enjoy staying in the countryside and driving to destinations nearby. I'd recommend you stay in Chianti so that you can both enjoy the countryside as well as have shorter drives to Siena, San Gimignano and the driving around the Chianti wine region. As you drive through the area, you'll find small towns along the way you'll end up stopping at - such as
Monteriggioni or Colle Val d'Elsa, or
Castellina in Chianti or
Greve in Chianti. Just know they are there and be flexible with your schedule, so you can see day to day as you go whether to stop or not. For places to stay at in Chianti, there are a few specific places I'd recommend you look at, but let me know if they're not what you're looking for and I can suggest different ones.
Here are a few you should consider:
Casolare di Libbiano is a B&B near San Gimignano:
http://www.tuscanyaccommodation.com/casolare-di-libbiano.html
Palazzo Malaspina, a B&B in San Donato in Poggio, near the Firenze-Siena highway:
http://www.tuscanyaccommodation.com/palazzo-malaspina.html
Tenuta Quadrifoglio has both rooms as well as apartments and breakfast is available for all, even if you're in the apartments:
http://www.tuscanyaccommodation.com/tenuta-quadrifoglio.html
As far as the best airport to fly into, that will depend on where you're coming from - there are two in Tuscany, one in Florence and one in Pisa which is just about an hour train ride from Florence. Both are convenient to fly into but of course if you do Florence as the first part of your stay it might be more convenient overall to fly into that one.
Check both when you're checking airfares!
Since this is getting really long, I'd better just post!!
