You can deep in the fairly atmosphere of Hobbits and Tolkien creatures at Vallombrosa (great place to find freshness and trees..) on the weekend.
You can admire the panoramic view from Forte Belvedere. Everyday.
You can enjoy knitting at Rifrullo's. On tuesday, the 3rd of July.
You can listen to some jazz music in Piazza dei Ciompi, near Piazza Santa Croce. Everyday.