Fiesole is just outside and above Florence. It is an ancient little town and great for a day trip (the ATAF #7 runs to Fiesole): nice walks, lunch in the Piazza Mino da Fiesole (try Perseus), roman ruins, churches - it has it all - plus amazing views on the Arno River valley and Florence. Unfortunately a giant public works project has had the piazza ripped up for years. The last time we were there, things were still looking pretty rough. Today we took a drive up for a walk and lunch with the kids since they were off from school, and the piazza now seems to be at least half way done - the construction walls are down for the most part, and you can see the statue of Garibaldi and Vittorio Emmanuel II (the link is to an old photo) having their famous handshake again. And the piazza will now be public space and not a car park as it used to be.
Unfortunately though, all around the Piazza Mino da Fiesole has just been repaved with nearly black macadam that takes a lot of charm out of the town. Paving streets had made a lot of news in Florence lately and has many Florentines upset. I don't know how it went over with the inhabitants of Fiesole - maybe their stone streets disappeared long ago - but it seems a shame that the comune could not come up with something better for such an historically important place.