June Wine Festivals
If you are going to be in Tuscany in June there is also the Montespertoli "Mostra del Chianti" that in 2015 runs from May 30th to June 7th. You could work it in around the Lamole and Radda ones.
Montespertoli is 30 miles southwest of Florence, a few miles off the main highway to Pisa, the FI-PI-LI. You take the Ginestra Fiorentina exit. This festival features high-quality wine from local producers and because it runs for over a week it also has other delightful activities during the course of festivities, food stands, concerts, live music, open-air theatre, parades, and an open-air restaurant in the main piazza.
This is a very pretty, hilly part of Tuscany, less dramatically mountainous than the main "Chianti Classico" area. It's worth a trip out this way from Florence to take in other nearby places such as Certaldo Alto (birthplace of poet Boccaccio), San Gimignano (for their famous Vernaccia white wine) and Colle di Val d'Elsa.