You can easily make days trips to Fiesole by bus and to Prato from Florence's SMN train station.
In order to reach Fiesole, just take ATAF bus n. 7 from the SMN train station which runs every 20 minutes starting at 6 am. The bus arrives right in Piazza di Fiesole.
The best way to reach Prato is by train, again from Florence's SMN train station. The journey takes about 20 minutes.