The Palazzo Vecchio is the most important civil building in Florence. Its construction began in 1299 at the request of Arnolfo di Cambio. Initially it was the seat of the Priors of the Arts and the Signoria and the home of the Grand Duke Cosimo I de Medici, until they moved to the Palazzo Pitti. During the period 1550-1565, Vassari completely decorated it to make it available to the ruling family. It now boasts a stunning interior, with its rooms and bedrooms, the living room of the Cinquecento, the Hall of Francesco I de Medici etc.
The Renaissance palace of Pitti is another thing that simply cannot be missed in the Tuscan city. Across the Arno river over most points of interest in the city, it's known just as much for its architecture as for its spectacular gardens. It also used to be a royal residence in the past.
The Palazzo Strozzi is a perfect example of a Renaissance palace. From the time of its construction until 1937, it was the property of the Strozzi family, but then it was acquired by the Istituto Nazionale delle Assicurazioni, which restored and transferred it to the Italian State in 1999. Currently it hosts two major cultural institutions, and offers contemporary art exhibitions. The courtyard has some amazing sculptures, and the cafe is one of my favourite places to have a drink in this wonderful city.