Fall is a good time to visit New York. The summer tourists are gone, and the weather is mild. Whether you want to see what’s new at favorite museums or check out lesser-known attractions, here are six ideas for enjoying a day in the city.

Museum of Arts & Design, 40 W. 53rd St.; 212-956-3535; madmuseum.org

These four floors in Midtown, with their swirled banisters and white walls, provide an elegant backdrop for a treasure of contemporary art. Skillfully crafted objects in its permanent collection range from spiral golden bracelets and modern sterling-silver-and-ebony tableware to colorful quilts and whimsical wooden sculptures. Through October 28, the exhibit “Inspired by China: Contemporary Furniture Makers Explore Chinese Traditions” pairs 27 masterpieces of historic Chinese furniture with 27 contemporary creations made for this exhibition.

Metropolitan Museum of Art, 1000 Fifth Ave.; 212-535-7710; metmuseum.org

This April, the Met unveiled its New Greek and Roman Galleries, and many of the 5,400 Greek, Roman, and Etruscan treasures returned to public view after years of storage. The Leon Levy and Shelby White Court for Hellenistic and Roman art, which houses much of the exhibit, resembles the garden of a Roman villa, with marble floors and a glass roof that allows artworks to be viewed in natural light. The atrium’s center features Greek and Roman statuary, including two huge statues of Hercules and a marble Dionysus, god of wine and revelry. Adjacent galleries feature two original rooms from Roman villas with wall frescoes, buried by the eruption of Mount Vesuvius in 79 ad and subsequently unearthed.

Fraunces Tavern Museum, 54 Pearl St.; 212-425-1778; frauncestavernmuseum.org

Just blocks from the South Street Seaport is Manhattan’s oldest surviving building, 54 Pearl Street, built in 1719 as a merchant’s residence. In 1762, Samuel Fraunces purchased the building and transformed it into a tavern, best known as the place where George Washington said farewell to his officers in 1783. The site is now a museum, with a permanent collection of historical paintings, newspapers, maps, and artifacts that relate to the American Revolution—including a lock of Washington’s hair. Through December, you can view “If These Walls Could Talk: 54 Pearl Street,” which chronicles the many incarnations of the building, from home to tavern to the offices of the Departments of State, Treasury, and War when New York was our nation’s first capital from 1785 to 1790.

American Museum of Natural History, Central Park West at 79th St.; 212-769-5100; amnh.org

There’s more to this museum than dinosaurs. In March, the museum reopened its restored Audubon Gallery, a hall with magnificent high ceilings. Originally opened in the 1930s, the gallery closed after the onset of World War II. The inaugural exhibit, “The Unknown Audubons: Mammals of North America,” on view through January 6, features rarely viewed paintings and lithographs by the famed master of nature artistry and his two sons.

On the first Friday of each month, the planetarium features Starry Nights—live jazz, free with museum admission. You can enjoy the concert with a glass of wine and tapas, available for purchase.

Frick Collection, 1 E. 70th St.; 212-288-0700; frick.org

The art collection of 19th-century steel magnate Henry Clay Frick is among New York City’s lesser-known treasures. Like Washington’s Phillips Collection, the museum offers a more intimate view of art than you get at larger galleries because it’s housed in Frick’s elegant former mansion.

The permanent collection includes works by Vermeer, Rembrandt, Fragonard, El Greco, Goya, Rubens, Whistler, Boucher, Turner, van Eyck, Holbein, and more. Marble sculptures by masters like Houdon, Venetian and Roman bronze statuary, and a collection of clocks, textiles, and tapestries also grace the mansion.

Museum of Modern Art, 11 W. 53rd St.; 212-708-9400; moma.org

Nearly three years after reopening, and almost double its prerenovation size, MoMA continues to dazzle visitors with its world-class contemporary art. Its huge atrium features monumental works like Monet’s “Water Lilies” and Barnett Newman’s “Broken Obelisk.” On the light-filled upper floors, you can view iconic artwork like van Gogh’s “Starry Night,” Matisse’s “La Danse,” and Picasso’s “Les Demoiselles d’Avignon.”

After seeing these masterpieces, treat yourself to a sophisticated meal at the Modern, which serves appetizers like cauliflower panna cotta with American paddlefish caviar and entrées like Maine lobster with buckwheat angel hair.

Every Friday from 4 to 8 pm, admission is free. At other times, adult admission is $20. A $30 MoMA/Top of the Rock combination ticket shaves 20 percent off admissions to MoMA and the observation deck two blocks away.