Back in the early Renaissance Medici were among the first to discover the joys of escaping the stone canyons of the city for the pleasures countryside. Many of the villas doubled as farms and hunting lodges. In the 17th century, Giuso Utens painted a series of lunettes of all of them with their gardens, now in the Palazzo Vecchio. In 2013, UNESCO placed them all on the World Heritage List.
The Elder Cosimo created the first, by commissioning his favourite architect Michelozzo to convert the family's 14th-century castles in the Mugello into residences, beginning with the Villa Medicea del Trebbio and the Villa Medicea di Cafaggiolo. Michelozzo also built Cosimo's beloved Villa Careggi, much closer to Florence, which became famous as the setting of the Platonic Academy.
Next came the first proper un-fortified residential villa, the Villa Medici in Fiesole, long attributed to Michelozzo but after recent scholarship the authorship points firmly to Renaissance man, Leon Battista Alberti.
We haven't included them all. Some are still privately owned but ones worth a visit around Florence include the Villa Artimino, Villa Medicea di Castello, Villa Medicea di Poggio a Caiano, Villa Medicea di Cerreto Guidi, Villa La Petraia and the gardens of Pratolino.