You are in tree-lined San Marco Square in the San Giovanni district, where memories of the Medici family abound, and where convent complexes of several religious orders are found, in addition to several universities. The Aula Magna, or Great Hall, and the Rectorate of the University of Florence face the square in a building that was originally the Grand Duke's Stable. If you see a long line, it's full of people eager to admire the original David by Michelangelo, which is kept in a Museum in the great complex that houses the Academy of Fine Arts.
Naturally the square gets its name from the church, which is connected to the beautiful Dominican convent of San Marco, and is also full of pigeons like its Venetian homonym!
Built at the end of the 14th century, it has a tall, sober façade from a much later period; in fact, it's from the 18th century, when the last of the many restorations and renovations that took place here were carried out. Today it is home to an enchanting museum dedicated to Fra Angelico, a poetic painter of the first half of the 1400s.
Inside, you'll see beautiful late-Renaissance architecture from the end of the 1500s, the same period that the side altar paintings and the bronze bas-reliefs of Giambologna date back to. You can find even older works here, such as the 14th-century frescoes of the interior façade and the beautiful 15th-century sacristy designed by the same architect as the nearby convent complex.
I'd also like to point out two excellent paintings by painters who resided in San Marco as Dominican monks: the Crucifix above the altar that's painted on a shaped panel is an early work by Fra Angelico, while the Madonna and Saints on the second altar to the right is by Fra Bartolomeo.
FUN FACT: the church floor is a masterpiece, and depicts all kinds of animals. Near the Chapel of St. Isidore you can see the effigy of a rhinoceros, which is a talisman against disease!