One day: from the Duomo to the Oltrarno
Start around the cathedral and the nearby streets. Then walk towards Piazza della Signoria. Along the way, you can see how the monumental centre blends with shops and everyday life. From there, head to the Arno and cross Ponte Vecchio into the Oltrarno.
Spend the rest of the day wandering around Santo Spirito without a fixed list of stops. If you still have energy, climb to Piazzale Michelangelo for a view over the city. The climb takes effort at the end of the day; staying by the river and sitting down to a leisurely dinner is just as good a way to finish.
With so little time, choose one place you really want to go inside. Moving from one museum to the next may leave you having seen plenty of art but with little sense of the city.
Two days: add art and an easy walk
Keep the first day as a chance to get your bearings. On the second, set aside the morning for the Uffizi Gallery if its collections appeal to you. Give the visit plenty of time rather than scheduling another major collection straight afterwards. When you leave, you can walk towards Santa Croce and explore the streets in that part of the centre.
If you would rather spend less time in museums, use the morning to visit a church or stroll along both banks of the Arno. Checking entry arrangements before your trip will help you decide which visits to book and which to leave open to chance.
Three days: look beyond the famous squares
On the third day, explore the San Lorenzo area and choose between the Accademia Gallery and other nearby places according to your interests. Continue towards Santa Maria Novella and leave room to step inside somewhere you discovered on the previous days.
Another option is to devote the day to the Oltrarno, with Palazzo Pitti and the Boboli Gardens at its heart if you feel like combining art with a walk. There is no need to fit both plans into one day. Florence is more enjoyable when you can linger at an important sight without watching the clock.
A week: alternate between the city and its surroundings
With a week, spread the major visits across days that also leave time for walking. You could spend the first three days in the centre, set aside a fourth for the Oltrarno and use another to return to your favourite neighbourhoods at a slower pace. Fiesole offers a nearby outing and a different perspective; Siena, Lucca or Pisa could each fill a separate day if you want to discover another city. Choose one rather than turning every day into a journey.
You do not need a car for this city itinerary. One may be useful if your week includes rural areas and scattered stops, but for exploring Florence and its main central sights, it usually brings the added worry of where to park. Before settling on a day trip, check transport options and access to the places you want to visit.
The most common mistake is planning each day as though walking, waiting, eating and resting take no time. Leave part of your itinerary unplanned. That freedom lets you find something of your own without expecting every hour to be memorable.