Archeological museum

The archeological museum has a lot of really neat exhibits, but my favorite by far is the chimera. It's an ancient Etruscan bronze depicting the legendary creature that was part lion, part goat, and part snake. Badass. Other exhibits include lots of other Etruscan bronzes, old pottery, and an Egyptian collection (complete with mummies!). Totally worth stopping by for just the chimera, in my opinion.

San Miniato

A fun little excursion is a hike to San Miniato. The large Romaneque church sits on top of a hill across the river from the city center, providing a beautiful panoramic of the city. Partway up the hill is Piazza Michelangelo, which offers a lovely lookout point. The church itself is very pretty, but my favorite part to visit is the graveyard. There are all sorts of elaborate monuments, tombstones, and mausoleums. Plus, it's a lovely walk up.

Medici chapel

The Medici chapel is attached to the church of San Lorenzo, next to the large outdoor market. The chapel is really impressive, with lots of beautiful inlaid stone designs (pietra dura) decorating the walls. The chapel is also the home of Michelangelo's Dawn, Dusk, Night, and Day statues on the tombs of two Medici family members.

Accademia

The Accademia houses Michelangelo's original David. There's a replica of the statue in Piazza Signoria where the statue used to stand. There are a number of other marble sculptures, including Michelangelo's uncompleted Schiavi, but David is clearly the main attraction.

I Fratellini

I Fratellini is a little sandwich shop in the middle of the city. They're cheap and delicious, definitely worth stopping by.


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Duomo

The Duomo is the symbol of Florence, and for good reason. It's construction marked the start of the Renaissance and it's just so cool. It's free to get in, although to be honest the interior is not as cool as other cathedrals, such as the ones in Pisa or Sienna. You should definitely climb to the top, though. There's a small fee to go up. It's absolutely gorgeous up there. There are 414 stairs, but it's all worth it.

Santa Croce

Santa Croce is one of the largest churches in town and my favorite steps to drink on. It sits on a large piazza that occasionally hosts fairs or markets. Inside you'll find the tombs of Michelangelo and Galileo, among others. Overall it's a pretty impressive structure.