I abstained so far from making a reply because the three estates which I have visited most often and would recommend, namely Fontodi, Vignmaggio and San Felice, are all deep into Chianti countryside along narrow winding roads.
However there is one of my future must-visit estates, namely Isole e Olena
http://www.thewinedoctor.com/italy/isoleeolena.shtml which is at Barberino Val d'Elsa some 10 km off the Florence-Siena highway. Another is Fèlsina
http://www.felsinawine.com/ , whose wines I buy regularly but have never visited, which is at Castelnuovo Beradenga close to the Siena-Perugia main road. Looking at the map, the latter seems closer to the main road.
The Florence-Siena highway is one of my least favourite in Italy and that is saying something. There are two quite narrow lanes with no hard shoulder for emergencies in each direction separated by a flimsy looking crash barrier and many tight curves and ups and downs. Yet many locals drive extremely fast well in excess of the speed limit (130 kph/81 mph on most Italian highways). Double check your mirrors before overtaking

.
PS: In Europe it is usually advisable to make an appointment when visiting a winery. One exception in Tuscany is Fonterutoli which is geared up for tourists and even charges for tasting

, very rare in Europe; it is, however, deep in the countryside.