Tuscany has several events all year round. Since you didn't mention what's the geographical are you are interested in, here you find the main events from June 17th to 25th across Tuscany:
June 17th - Palio di San Ranieri Pisa - tradition regatta on the Arno river in Pisa for San Ranieri, patron of the city.
June 18th - The Joust of the Saracen Arezzo - la Giostra del Saracino is a medieval tournament with knights, horses and beautiful historical costumes.
June 18th and 19th - Ferie delle Messi San Gimignano - medieval harvest festival of the people of San Gimignano. There are medieval games, knights, historical parades.
June 24th - San Giovanni Celebrations Florence - San Giovanni is the patron of Florence, that celebrates him with a colorful parade and with great fireworks at night.
These events take place every year. For other events, such as local fairs and food festivals, as well as other local events, there is no calendar yet because it's really early. In fact local events, such as typical "sagre" or food festival, are generally advertised and communicated just 2-3 weeks before they will take place.
The best thing to do is you go directly to local tourist offices and ask for the events' calendar. I also suggest you read our blog about Tuscany on Fridays when we publish a post on the best events in Tuscany, together with suggestions for spending the weekend in Tuscany. I also recommend you have a look at our Tuscany events' calendar that we update on a regular base.
I hope these suggestions helped you. Don't hesitate to come back with any question