Photo: Sailko, CC BY-SA 3.0 via Wikimedia Commons
The Etruscan art collection is particularly good.
The National Archaeological Museum of Florence is an archaeological museum in Florence, Italy. It is located at 1 piazza Santissima Annunziata, in the Palazzo della Crocetta, a palace built in 1620 by Giulio Parigi for princess Maria Maddalena, daughter of Ferdinand I de Medici.
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Accademia Gallery
Highlights are Michelangelo's original David (the one in Piazza della Signoria is a copy) and his unfinished Slaves. It also includes Florentine painting, a museum of musical instruments, and Russian icons. No photography is allowed inside. N.B. the "Accademia di Belle Arti" next door is a university department, not connected with the Gallery.
Houses frescoes by Fra Angelico and his workshop. Fra Angelico painted a series of frescoes for the cells in which the Dominican monks lived.
Offers a wide choice of Italian language and culture courses for children and adults from beginning to advanced levels.
Cimitero degli inglesi
In the 19th century, the "English Cemetery" received anyone that the city's churchyards wouldn't receive, e.g. Orthodox Christians, but Britons and Americans were the majority. Famous names here include Elizabeth Barrett Browning, Fanny Trollope and Beatrice Shakespeare, a relative of William. There are lots of ornate gravestones with flowery inscriptions in multiple languages.
Sinagoga e Museo Ebraico Firenze
Lovely Moorish-style synagogue built in 1882 and a museum with many artefacts and documentation of Florentine Jewish life going back many centuries; audio tours in multiple languages are available.
Duomo
The cathedral interior is to a basilica pattern; it's vast and at first feels dark and empty. Give your eyes time to adjust, and admire the stained glass windows, funeral monument of Bishop d'Orso, and altar of St Zanobius. Below is the Crypt (M-Sa 10:00-17:00) with remains of the preceding cathedral of Santa Reparata, and the tomb of Brunelleschi. Giotto is believed to lie here somewhere, but his tomb has yet to be identified. Above is the soaring cupola or Dome. The cathedral is free, but you need a pre-booked ticket and time-slot to climb the 464 steps up to the Dome (entrance north side of the church). Slots are available M-F 08:30-19:00, Sa 08:30-17:00 and Su 13:00-16:00.