For serious shoe enthusiasts, this museum, in the basement of the Ferragamo Boutique, displays the designer’s classic shoes, some worn by the likes of Marilyn Monroe, Greta Garbo and Katherine Hepburn. Profits from the museum fund scholarships for aspiring shoe designers.

In business since 1612, this combination perfumery/pharmacy still sells remedies, dietary supplements, smelling salts and digestive aids, based on concoctions developed by the monastery’s Dominican friars since 1221. A variety of potions purport to cure ailments such as hysterics and joint pain, as well as assisting in weight loss. A free museum goes into the history of perfumery/pharmacy.

Spanning the Arno River at its narrowest point, the “old bridge” is as storied as it is picturesque (and overrun with crowds). First documented in the late 10th century, the bridge was destroyed by flooding in 1177, 1333 and narrowly avoided being swept away during the flood of 1966. The current structure dates from 1345. Ponte Vecchio was the sole...