On a trip to Tuscany in 2012, I tried to get to as many of the medici villas and gardens as possible. As it was before their inscription (in 2013), most villas were not well indicated and most were closed to visitors. So for some, it was more getting a glimpse of a villas than a real visit. Here is a list of the 10 villas I managed to see:

Boboli gardens are within « Historic Center of Florence » WHS. So it is inscribed twice. The gardens are nice to wander around. The site includes the Pitti Palace, a vast Renaissance palace housing a museum. A top the gardens, the Casino del Cavaliere, a nice small separate gardens.

Villa Petraia garden and villa is open to public, and easy to reach from Firenze center. It is a nice walk around the Italian gardens.

Villa Castello is about 5 minute from villa Petraia. It is usually open to public, but was closed on the day of my visit. I could see the extrenal walls of the villa. The gardens seem very interesting to visit.

Villa Pratolino is a few kilometer north of Florence centre, in the middle of a hospital campus. It is closed to visitors and the villa is hidden behind trees.

South of Florence city, Villa de Poggio Imperiale can be reached by bus. It houses a high school. The front of the building is a parking lot. This villa can be ommitted.

Villa Fiesole i a few kilometer east of Florence, accessible by bus. The village of Fiesole is on top of a hill, with great views on Florence and its valley. The villa is not open to visitors and is behind walls, so you can only get a glimpse of it.

The others villas are further afield and recquire a car, as public transportation seems difficult from Florence.

To the north, villa Cafaggiolo is a one of the oldest villa, looking like a small castle (my picture). It is not open to the public, but is easy to look at from the public road. On a hill nearby is Villa Il Trebbio, accessed by a long dirt road. Unfortunately, the villa is closed behind wall and trees.

To the west of Florence, villa Poggio a Caiano is a very nice villa and garden, both open to public. Villa La Maggia can only be seen from outside, from a public park a bit west. There is however a guided tour once a month to the inside.

Villa Cerreto Guidi houses a small and free museum on hunting. It is in a small village atop a hill. Thanks to the museum, the villa can be extensively visited. To note, a few kilometers from here, the village of Vinci, birthplace of Leonardo.

Villa Artimino houses a conference center and a small museum (only open in the morning). Nice view from the road however.

To summerize, I would recommend Villa Petraia and Castello by public transport from Florence, and Villa Poggio a Caiano and Cerreto Guidi by car.