I do not know how many of Lorenzo di Medici's country villas are extant, but he helped design a few of them, one of which was an architectural inspiration for Palladio.
This one, sitting on the hills overlooking Florence, was built by Cosimo for his second grandson Giovanni, and came into Lorenzo's hands after his brother was assassinated by a cabal which included the Pope. It became one of Lorenzo's favorite hangouts with his philosopher, artist, and poet pals (and girlfriends).
(By the way, we recommend staying in Fiesole when visiting Florence, and it's just a 15-minute bus ride down the hill. November and May are good months.)