The Scuola del Cuoio is right behind (actually it is attached to) the church of Santa Croce. It is both a leather school and shop, offering a variety of courses and hand made leather goods for sale, and has been run by the same family for nearly 60 years. This recent article describes the school in more detail. There is an entrance off of Via San Giuseppe, or you can enter the school directly through the Church. Worth a visit, especially if you are leather shopping.
Scuola del Cuoio: Piazza Santa Croce 16, Florence; 39 (055) 244-533; http://www.leatherschool.com