Two important banal facts to be clear immediately:
1) Florence is beautiful.
2) Florence is frightfully submerged by tourists; whole fleets that occupy whole streets as if they were a single indistinct body and that roam the city with mobile phones, selfie sticks, iPad, etc. Joys and pains of mass tourism.
Continuing in the banalities, so many places to see; I will quote them randomly:
the Cathedral of Santa Maria del Fiore (the “Duomo“)
Palazzo Vecchio with his David
the adjacent Uffizi Gallery
Piazza della Repubblica, where the Gilli pastry bar is located
the Basilica of Santa Croce
Piazza della Signoria,where one of the best pastry shops in Florence is located: Rivoire
The Old Bridge
and still other magical places.
unmissable, crowd apart.
A couple of tips about hotels and restaurants:
1) Hotel Home: slightly outside the historic center but better because quieter. Beautiful terrace to admire the whole city
2) the Cantinetta delle Terme: Fish and meat menu with obviously a good Florentine steak. Very nice location in a quiet street of the historic center
3) Antico Ristoro di Cambi: On the less famous shore, in the district of San Frediano. Excellent Tuscan cuisine. 900 meters from the Santa Maria Novella Station.