"for other landmarks to visit afterwards".....
The whole of Florence is made up of so many landmarks that (as Eugene M says) your dilemma will be what not to see.
Galleria dell'Accademia - Academy Gallery - MichelAngelo's Statue of David etc.
(This is not in the Uffizi as some people believe)
Museo di San Marco - the frescoes of Fra Angelico
Church of Santa Maria del Carmine - Brancacci Chapel
Church of Santa Maria Novella
Museo dell'Opera di Santa Maria del Fiore
Wherever you walk in this beautiful city, you will find works of art on every street corner - don't forget to look up as well as in front of you.
Edited: 6:56 pm, December 25, 2012