New York attractions: The Metropolitan Museum of Art (SLIDE SHOW)

The impressive facade that characterizes the Met’s beautiful Fifth Avenue exterior was actually not part of the building’s original look: The museum was conceived by Calvert Vaux and Jacob Wrey Mould as a small, red-bricked building in the neo-Gothic style, complete with a steel-and-glass roof. As the museum’s collection expanded, so did its physical presence: In 1895, Richard Morris Hunt designed the splendid Beaux Arts entry wing, which runs along Fifth Avenue.

The entry wing and the Great Hall were opened to the public in 1902, much to the delight of New Yorkers. The Evening Post called it “the only public building in recent years which approaches in dignity and grandeur the museums of the old world.” The various additions to the museum’s facade now completely surround the original structure—the Met is now housed within a 2-million-square-foot building—but you can still peep parts of the original structure from the inside.

Each year, the museum selects a different artist to design a installation for its gorgeous Iris and Gerald B. Cantor Roof Garden. This year’s pick has already become a new favorite: The minute you step into Tomás Saraceno on the Roof: Cloud City (through Nov 4), your perception of the world around you completely changes. Built with a stainless-steel frame, transparent acrylic floors and mirrored panels, the sculpture reflects the Central Park landscape, the roof terrace and the sky, offering the viewer a kaleidoscope of unique and unusual perspectives.

As the expansion of the Met continued and the museum acquired more collections, Thomas P.F. Hoving, who was appointed director in 1967, decided to add six new wings to the museum with the help of architecture firm Kevin Roche John Dinkeloo and Associates. This expansion, completed in 1990, included the Roof Garden. The Met Roof Garden Café and Martini Bar also provides an unbeatable place to enjoy an alfresco cocktail after wandering through galleries.

The Met’s first-floor Arms and Armor Gallery houses a staggering collection of armor from all around the world, including an impressive European section. That gallery comprises fantastic armor from the late Middle Ages, complete with chain mail, full horses’ armor, axes and swords.

The museum’s collection of Medieval and Byzantine Art is kept in the Main Building. There, take a moment to inspect a wrought-iron choir screen from the Cathedral of Valladolid. Installed in the Spanish church’s central nave in 1763, the grand piece was likely crafted by artisan Rafal Amezúa. Nearby, beautiful book covers, tabernacles and elaborate scriptures capture the work of dedicated monasteries. You’ll also find fantastic examples of stained glass and intricate tapestries here.

In the ground floor’s north wing sits the collection of Egyptian art and the glass-walled atrium housing the stunning Temple of Dendur, moved en masse from its original Nile-side setting and now overlooking a reflective pool.

The Met offers a whole other world to those who venture a train ride farther uptown: The serene and mystical Cloisters museum and gardens overlooks the Hudson river and is nestled in Fort Tryon Park in northern Manhattan. It opened to the public in 1938, and contains an extensive collection of medieval art and architecture.

The Cloisters was originally a museum of medieval art and architecture assembled by George Grey Barnard; the Met acquired the collection in 1925 with funds provided by John D. Rockefeller. The building itself incorporates architectural elements of five medieval cloisters in France—architect Charles Collens built around the original structure in order to display approximately 3,000 works of art from medieval Europe, dating from between the 9th and 16th centuries.

The galleries at the Cloisters are organized by date, moving from the Romanesque through the Gothic periods. Don’t miss the celebrated “Unicorn Tapestries,” as well as illuminated manuscripts, stained-glass windows, sculptures, enamels and metalworks.

The collection at the Cloisters keeps growing, in part due to an endowment left by Rockefeller and other philanthropists. The Cloisters’ chapels and exhibition halls contain more than 5,000 works of art, and visitors can admire masterpieces such as mid-13th-century a stone Virgin from the Strasbourg Cathedral in France, as well as an elaborately carved ivory cross from the 12th century, originating from the English abbey of Bury St. Edmunds.