3 days is perfect for a Florence visit
If you just want to see the main attractions, you can fit these into one day of exploring Florence. However, if you want to appreciate the city a little more, 3 days in Florence is not too long to allocate for your visit, as there is much that the city and the surrounding area has to offer. Here is what three days in Florence might look like:
Day 1 - Duomo and a gallery
Your first day will probably be dedicated to visiting the Florence Cathedral (Duomo) and the other attractions in the Piazza del Duomo. After that take an easy non linear walk through the San Lorenzo Market and the Piazza della Repubblica, to the hub of Florentine life in the Piazza della Signoria where you can visit the Palazzo Vecchio. If you are passing through the San Lorenzo Market, you can browse Florence's famous leather products.
Day 2 - A gallery and Oltrarno
On your second day, you will probably still want a taste of art and culture, so start by going to whichever major museum you did not make it to one the first day (either the Accademia or the Uffizi). If you visit the Accademia on this day, you can follow it by visiting one of the lesser known museums around the corner called Opificio delle Pietre Dure museum.
The other beautiful part of the city is in the Oltrarno district across the river. This part of the city is characterized by the many artisanal workshops where you can find beautifully handcrafted souvenirs if you did not buy anything in the San Lorenzo market the day before.
You should also allocate time for a trip to the Pitti Palace and the surround Boboli gardens. If you want to spend more time in museums, you could take your pick of the 5 Pitti Palace museums and spend the rest of afternoon wandering away from the heat of the day.
Day 3 - Wander in Florence or take a day trip
On your third day, there are several different ways that you could plan it. The first option would be to spend the day going to lesser known museums and galleries (and there are plenty of them).
You could go to the Bargello National Museum if you have no had your fill of art and sculptures, or you could go see the Museo Galileo for a more hands on experience of the local history. You could also go see more off the beaten track places like La Specola Anatomical collection, or just walk through the medieval streets surrounding the Piazza del Duomo.
Alternatively, you could take an easy day trip from the city of Florence. Florence is in the heart of the Tuscan countryside, so there are many easy day trips you could take if you want to escape the historic centre and see more of the surrounding area.