I did exactly this last year and it was amazing.

LCY - FLR definitely easiest and gets you into the thick of the Tuscany action quickly without messing about in Pisa as you would if flying from LHR or LGW.

Our route was something like this:
drive down to Siena, stay in an agriturismo near the city for 2 nights.
drive down to Montepulciano area, 2 nights in another agritusmo round there
drive up to Greve in Chianti area, stay on a vineyard for 1-2 nights
drive into central Florence, return the car and walk to hotel. Stay 1-2 nights. Florence is wonderful but felt like a relative dump compared to the other amazing places mentioned above.

Thoroughly recommend the trip, very easy and amazing scenery. And the food and wine...