La Bottega di Volpaia near medieval village of Volpaia (+39 0577 738001) - La Bottega is a restaurant with an authentic menu, garden fresh produce and a beautiful setting with valley view. Definitely book ahead at this one!!
La Perla del Palazzo in Radda (+39 0577 735640) - La Perla del Palazzo, in the historic Palazzo Leopoldo, provides an excellent Tuscan menu in an elegant dining room or charming garden. They also do cooking lessons if you'd like to learn to re-create their delicious dishes.
Le Forchette del Chianti in Radda (+39 0577 738923) - Le Forchette is another place to pair quality red and white wines with Tuscan specialities.
Venturing a bit further, but still in the Chianti region, you might try:
Badia a Coltibuono near Gaiole in Chianti (+39 0577 74481) - Literally 'the abbey of good harvest', you know that the restaurant on the grounds must live up to its name, and this one does. Delicious Tuscan dishes done with flair and a little something extra. With a breathtaking view from the outdoor dining terrace and wine-tasting menus paired with their dishes.
La Bottega del Moro in Greve in Chianti (+39 055 853753) - Now located in Greve's historic piazza, La Bottega is a family-owned restaurant that feels like home and whose dishes are authentically delicious.
Antica Trattoria La Torre in Castellina in Chianti (+39 0577 740236) - La Torre is located in the central piazza of Castellina and serves food that has made this area famous.
Solociccia in Panzano in Chianti (+39 055 852727) - Though they do have a vegetarian menu, Solociccia is for the serious meat-lover. For €30/person they serve a full meal where the stars of the show are its 6 meat courses.