There are many museums in Florence beyond the Uffizi and Accademia Galleries. Museums in Florence are can be divided into 3 types: those run by the Italian national government, which are called State museums, those run by the city which fall under the Florentine Civic Museums office (see the list of those here) or private (such as the Palazzo Strozzi, the Horne museum, the Stibbert Museum).
In order to help you sort out which are which, I've created a list below of the STATE MUSEUMS. This is particularly important when special openings occur or when free entry is offered into State museums only (which will not include the Civic museums). For this reason, it is always handy to understand which are which.
** ALL OF THE STATE MUSEUMS below offer FREE entrance to everyone on the FIRST SUNDAY of every month!! City museums do something similar, but ONLY for local residents. **
To further complicate some matters, since summer 2014 the state museums in Florence have been split up into 4 independent entities that control the museums under each, thus in theory creating their own policies separate from national policies. For now, both the Uffizi Galleries and the Accademia Gallery have continued to follow general Italian state policies, although prices for admission have changed in 2018.
- Uffizi Gallery (now called the Uffizi Galleries, which also includes the Pitti Palace and Boboli Gardens. The Contini Bonacossi Collection has now been integrated within the Uffizi Gallery collection)
- Accademia Gallery (+ Cherubini Conservatory Musical Instruments Collection)
- Bargello National Museum
- The Medici Chapels
- Museum of San Marco
- The Pitti Palace
- The Palatine Gallery & Royal Apartments
- The Gallery of Modern Art
- The Museum of Costume and Fashion
- The "Treasury of the Grand Ducks": The Medici Treasury also known as the Silver Museum
- The Porcelain Museum
- The Boboli Gardens
- Museum of Palazzo Davanzati
- Museum of Casa Martelli
- Church and Museum of Orsanmichele - free entrance
- Hall of Perugino - free entrance
These are also museums run by the Italian State, but I'm separating them out because they often have hours that change and apply only to them. They are often called the "Medici Villas".
- Garden of the Medici Villa of Castello - you cannot visit the inside of the villa
- Corsini Villa of Castello
- Medici Villa La Petraia
- Medici Villa of Poggio a Caiano and Museum of Still Life
- Medici Villa of Cerreto Guidi and its Historical Hunting and Territorial Museum
The Last Suppers and Cloisters
These are smaller State-run museums in Florence that pertain to a small area within cloisters/churches and are all free entrance.
- 'Cenacolo' of Ognissanti - Last Supper of Ognissanti
- 'Cenacolo' of Andrea del Sarto - Last Supper of San Salvi
- 'Cenacolo' of Fuligno
- 'Cenacolo' of Sant'Apollonia - Last Supper of Sant'Apollonia
- Cloister of the Scalzo
- The Carriage Museum (Pitti Palace)
- The Vasari Corridor (Uffizi Gallery) - closed for restoration as of November 2016 until further notice.