Florence is blessed with some of the world’s greatest treasures: Botticelli’s zaftig Venus, Raphael’s elegant Madonnas, the soaring Duomo. But there’s more in this Renaissance capital than meets the public eye—in fact, some of its most impressive works aren’t out on display. They are tucked inside monasteries or schools, locked behind family-owned gates or shut away in museum annexes for lack of security funds.

Still, with time and patience, anyone can book an appointment to see Florence’s largest private garden or a library Michelangelo designed for the Medici family. Enlisting professional help will spare you pleading phone calls, emails and sometimes even faxes. (Luxury travel agency Red Savannah and the concierge at the Hotel Savoy helped me.) Plan at least two months in advance. “Accept the very small windows of opportunities that are going to come,” said Sarah-Leigh Shenton, marketing director at Red Savannah. “Don’t try to negotiate for a nicer time so you can have a leisurely breakfast.” Here are five of the city’s most special “by appointment only” sites. If you score a slot, you might just be the only visitor of the day.

Contini Bonacossi

Entering the building where this collection is stored feels like going into a bank vault—visitors pass through a series of locked doors into a set of small, bland rooms. The artwork is certainly worth guarding: In the collection are a marble statue of St. Lawrence writhing on a gridiron (the only Bernini sculpture in Florence), an unrestored El Greco and one of Veronese’s most lively paintings, an upper-class man keeping his son from stepping out of the frame, shown above. The works belonged to Alessandro Contini Bonacossi, an art dealer who was convicted of being a fascist and Nazi collaborator after World War II. When Bonacossi died in 1955, he left some 1,000 pieces, including works by Tintoretto, Bernini and Veronese, to Italy. After his heirs challenged the will, the public was left with these 35 objects. Via Lambertesca, uffizi.org

Vasari Corridor

Dan Brown’s novel “Inferno” brought fame to this kilometer-long passageway that stretches across the Arno River, from the Palazzo Vecchio and Uffizi Gallery on the northern bank to the Palazzo Pitti on the south. The upside: It’s easier to get an appointment to traverse the hall these days. The drawback: A rare experience is becoming common.

Named for its designer, Giorgio Vasari, the corridor was built by the Medici family in 1564 so they could travel privately between their home (Palazzo Pitti) and the seat of government in the Palazzo Vecchio. Before the elevated hall was constructed along the Ponte Vecchio there was a meat market on the bridge; the Medici did not relish the smell, so the market was replaced with goldsmithing, which you can still see there today. Now part of the Uffizi, the corridor is lined with self-portraits, including some interesting ones by Bernini and Ingres. But the best part of visiting is the vast, meditative views of the Arno. Tours start from inside the Uffizi or the Boboli Gardens. uffizi.com

Laurentian Library

This might just be the most exciting architectural space in Florence. Designed by Michelangelo for Medici Pope Clement VII in 1523-24, the library has influenced artists for centuries—Mark Rothko, for one, said that it informed his 1950s Seagram Murals. The library is in a cloister inside the Basilica di San Lorenzo di Firenze, one of the city’s largest churches. You enter by stepping into a small, dim vestibule with 44-foot-high ceilings. The room’s height is intimidating, as is the massive, steep stone staircase on one side. That tension is part of the genius of its design—ascending to the reading room is, in a way, like passing from anxious ignorance into civilized calm. The airy space is topped by a gold and red ceiling and lined with two rows of carved reading benches. Books were once attached to them by chains, but are now kept in humidity-controlled storage. Piazza San Lorenzo, 9, www.bml.firenze.sbn.it

Torrigiani Garden

Hidden behind high yellow walls, this 17-acre private garden is by far the largest in Florence. It was laid out in the early 1800s, at the height of the Romantic period, and features meandering paths, as well as follies like a 98-foot-tall stone tower. Sculptures are scattered throughout the garden—one of the Egyptian god Osiris, another of a lion attacking a bull. Tours are usually led by members of the Torrigiani family; if you’re lucky, you’ll get personal perspective on what it’s like to own a piece of land for centuries. Via dei Serragli, 144, giardinotorrigiani.it

Villa I Tatti

In the early 20th century, Bernard Berenson, an American art historian, bought an unremarkable farmhouse on the border of Florence and Fiesole, and turned it into a Renaissance-style villa surrounded by 70 acres of olive groves and gardens. Today it houses a Harvard institute for Renaissance art, in addition to the late Mr. Berenson’s art collection and library. Religious paintings are arranged salon-style on the walls; pieces of centuries-old altars are scattered throughout the quiet halls and rooms. Among the collection’s highlights are a terrifically moving “Entombment of Christ” by Giotto, depicting a disciple kissing the dead Christ, and a joyful “Madonna and Child with Goldfinch.” The grounds are considered so historically important that their preservation is mandated by law. Via di Vincigliata 26, itatti.harvard.edu