Once you arrive you must visit the Ponte Vecchio as the shops are opening (around 9am) in the morning. Capturing great morning light as the city starts to wake up slowly.
Take a nice walk along the river on the Oltrarno towards Costa San Giorgio. This street has many gorgeous views of Florence. You will walk up the this steep street but remember to turn around and take in the sights. If you have trouble walking, take your time going up this street towards the Porta San Giorgio. On this street as well, Galileo once lived. You will see the plaque on the left hand side of the street as you get closer to Porta San Giorgio.
Come back over to the city center side and visit the Uffizi Gallery where you can experience the great masterpieces of the Renaissance era. Next door there is Museo Galileo which was renovated within the past year and has many great exhibits. See the objects Galileo used and how they were used in the science of war and navigating around the Mediterranean sea.
Once you get to Piazza del Duomo, follow the line of people who are waiting to see the top of the Duomo. It is a 360 degree view of the city of Florence. There are 463 steps to reach the top, remember to soak in the views. Don’t forget your camera. Afterwards, reward yourself with a fresh and delicious panino from Luca and Leo at Vinaino di Parte Guelfa. If you feel like a more filling meal, head to Pangies for the evening after a walking around Florence.
One last jewel you should visit in Florence is the small little church of Santi Apostoli. My favorite place in the city to sit and reminisce on life. This church has been around since 805 and was founded by Charlemagne. It has survived 2 floods, fires and many damages during the war and it is still standing.
Even if you are only in Florence for one day, you can pack in many grand views, sights and experiences.