This little town, almost a village, is just outside of Florence. You can get there by one of the city buses easily enough. For me is it was a wildcard visit. I had no idea what would await me and was pleasantly surprised.
During the ride, I sat near a woman from the Philippines. She has been in the area for over 20 years and works as a servant in one of the nice villas in Fiesole. Her employer paid her well and treated her very nicely. We had a good talk and she went off to work as I began exploring the town.
One thing which may be worth a visit, if you like archeology, are the Roman ruins in Fiesole. You have to pay to get in, which supports the place (fair enough).
Surrounded by hills and quite exclusive. Had my father retired in Italy, Fiesole is the kind of place, where he would have bought a villa. Average cost of a home is 3 million Euros. It's quiet, nice and the people are friendly. I liked it and should I ever go back to the area, would rent a room for a couple months here as a base to work from.
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Use a bus
From Piazza San Marco, get the bus number 7. Note that the bus website was out of date and showed a different number bus when I was in Florence. There is a small sort of information kiosk where you can ask (in case they have changed the number again).
I enjoyed my time in Fiesole and was glad I took the effort to reach it.