A 2 day trip is quite enough or a Florence visit. Here is a summary of what you can hope to achieve depending on how much time you decide to spend in Florence.
Hit the high points of Florence. Quick visits to Duomo, Uffizi, Galleria Accademia, Ponte Vecchio, and gelato in the streets.
Enough time to tour the Uffizi, climb the cupola of the Duomo, visit Piazzale Michelangelo, have a Bistecca alla Fiorentina.
Explore Florence districts and attractions beyond the centre. Wander in Oltrarno, take in some relaxed nightlife, or visit nearby Fiesole. Shop for souvenirs in local markets.
Day trip around Tuscany, or a wine tour in Chianti
Themed tours of Florence to understand the Medicis, Michelangelo, or The Renaissance period.
Florence in 1 day
If you only have one day to spend in Florence, I recommend you stick to the city center. First, I would purchase a guidebook which gives you details and some background of the main sights in Florence. This way you can traverse the city while taking it in with every step. However, you should avoid visiting inside many of the main attractions as the lines can be extremely long. For example, reaching the top of the Cupola can take up to half a day. You should make sure to visit all of the main churches and squares. Of course, don’t miss the riverside or the Boboli Gardens.
Florence in 2 days
If you have two days in Florence, in addition to visiting the main sightseeing spots you can go shopping at Mercato Centrale di San Lorenzo, Via Tornabuoni, and Via dei Calzaiuoli. During the day you can take a walk to Le Cascine. For some variety, you can also take a longer walk to Piazzale Michelangelo, which is beautiful at night.
Florence in 3 days
If you three days in Florence, your options start to increase. This is enough time delve deeper into Florence’s rich history. You should wake up early and go to the top of the Duomo or the Campanile. You should also go inside the main churches (Santa Maria del Fiore, Santa Croce, Santa Maria Novella, and Santo Spirito). Another option is to hire a guide in order to gain a deeper understanding and appreciation of Florence. Of course, remember to visit Fiesole in the evening.
Florence in 4 days
With four days, you have even more options. There are four main quarters in the old town. This means you can split your visit up and tour a quarter a day. Or you could tour the old town over the course of two days, followed by a day tour outside of Florence. Good choices include Siena, Pisa, the Chianti area, San Gimignano, Mugello, and Monteriggioni. You could also experience the nightlife by spending a night in one of Florence’s clubs, such as Space Electronic.
Florence in 5 days
If you are lucky enough to have five days to spend in Florence, you can not only appreciate Florence, but also the surrounding area. Some good options include booking a wine tour in Chianti or taking a trip to one of the main cities near Florence. You will also have time to visit museums such as the Uffizi and to enjoy dinner at one of restaurants serving Bistecca Fiorentina. You can even enjoy a day at a spa in Chianciano Terme, located near Siena.
At least three days, in my opinion.
Day 1 - I personally love art, so I suggest you take one day only to go and visit the Uffizi.
Day 2 - Another must-do is, of course, the Duomo and the Battistero. Also, the Chapels in San Lorenzo, the Cappelle Medicee, are mandatory. I think this would take another day.
Day 3 - If you want you can have a third day to go shopping around or to go and see the most beautiful areas of the city, such as San Frediano and Santo Spirito!