Ticked off New York City’s big sights and wondering where to go next? From sinking a pint in Brooklyn’s Red Hook to sampling Italian delicacies in The Bronx, Stephen Keeling picks the city’s off-the-beaten track highlights.

1. Sample small-batch Red Hook

At the southern tip of Brooklyn, the cobblestoned blocks and red-brick waterfront warehouses of Red Hook feel like a totally different city. The area is sprinkled with artsy stores, no-frills cafés and small-batch food and drink producers. Take a tour at Red Hook Winery, grab a tasty treat at Steve’s Authentic Key Lime Pies or feast on sumptuous pit-smoked barbecue at Hometown.

On summer weekends, head over to the Red Hook Ball Fields, where a dozen or so Latin American food carts and vendors set up around the local football (soccer) field. End the day at Sunny’s Bar, the neighbourhood’s spiritual heart, an old-school dive that opened in 1890.

Sunny's Bar in Brooklyn, New York CityWaywuwei/Flickr

2. Pay tribute to a giant of jazz at Louis Armstrong’s House

The multicultural borough of Queens rarely features on mainstream tourist itineraries – and few visitors know that the great Satchmo lived here from 1943 until his death in 1971. In fact, Dizzy Gillespie lived near Armstrong, and Ella Fitzgerald, Count Basie, Lena Horne, Fats Waller and, briefly, Charles Mingus all called the borough home too.

The jazzman’s legacy is preserved at the Louis Armstrong House Museum, where guided tours showcase Armstrong’s trumpets, furnishings and other personal belongings, enhanced by rare audio recordings made in this very spot. The visitors’ centre across the street holds a fascinating collection of Armstrong’s personal archives.

Louis Armstong's grave in Queens, New York CityWally Gobetz/Flickr

3. Discover Brooklyn’s flea markets

New York’s most fashionable borough is a fun place to shop. The Brooklyn Flea is the undisputed king of art, craft and antique markets, but there are several equally as enticing (and less touristy) alternatives.

The Brooklyn Makers Market showcases the work of craftspeople across the city, while Artists & Fleas is a slightly posher artist, designer and vintage market. For a grungier blend of live music, tasty food, art, jewellery and tattoos try Rock N’ Shop in hipster enclave Bushwick, or Shwick, the huge arts and crafts warehouse in the same trendy neighbourhood. Some markets run seasonally or appear on an irregular basis, so check their websites for the latest dates.

Flea market in Brooklyn, NYCShinya Suzuki/Flickr

4. Explore the city’s Jewish roots at the Museum at Eldridge Street

Surprisingly few tourists make their way to the Museum at Eldridge Street, tucked away in a section of the Lower East Side slowly being absorbed by Chinatown. Completed in 1887 as the first synagogue for Eastern European Orthodox Jews in the USA, this painstakingly restored site is a grand brick and terracotta hybrid of Romanesque, Moorish and Gothic influences.

The real highlight is the main sanctuary upstairs, with rich woodwork, a painted ceiling and giant chandelier, and original stained-glass windows, including the west-wing rose window – a spectacular Star of David roundel. The synagogue is a functioning house of worship, but you can visit the interior on guided tours, which provide plenty of entertaining stories about the neighbourhood.

Museum at Eldridge Street, New York CityPaul Stein/Flickr

5. Stroll the streets and parks of Fort Greene

Brooklyn Heights and Park Slope get most of the attention across the East River, but traditionally African-American neighbourhood Fort Greene is crammed with equally gorgeous, nineteenth-century architecture.

Author Richard Wright is memorialised in leafy Fort Greene Park, designed by Frederick Law Olmsted and Calvert Vaux, while South Portland Avenue is one of the prettiest streets in all of New York City. Adjacent South Elliott Place is home to Spike Lee’s Forty Acres and a Mule filmworks. If you’d rather go with experts, Big Onion Walking Tours offers an excellent introduction to the area for a reasonable price.

Fort Greene Park, New York City, USACisc1970/Flickr

6. Soak up the art at the Hispanic Society

Stranded in Upper Manhattan’s Washington Heights, the Hispanic Society of America sees only a trickle of visitors, despite holding some of the city’s greatest artistic treasures.

Part of Audubon Terrace, a Beaux Arts folly completed in 1908, the society owns one of the largest collections of Hispanic art outside Spain. The main, dimly lit gallery glows with the rosy hues of a Castilian palace.

Admire classics from El Greco, including his Holy Family, and typically expressive portraits by Velázquez and Goya. The building is also home to 14 giant murals by Joaquín Sorolla y Bastida – his Vision of Spain was commissioned specifically for the society in 1911.

Artworks in Hispanic society building, New York CityGigi_nyc/Flickr

7. Trawl the Italian trattorias and bakeries on Arthur Avenue

“Little Italy” in Manhattan is little more than a tourist mall these days, and New York’s largest Italian-American community actually lies smack in the middle of The Bronx.

Arthur Avenue is the main thoroughfare of foodie paradise Belmont, lined with pasticceria, authentic Italian restaurants and gourmet delis that make their own rich sauces and spicy sausages. Try Cosenza’s Fish Market stall for fresh clams and oysters, Madonia Brothers Bakery for olive bread and cannoli, and DeLillo Pasticceria (once owned by author Don DeLillo’s parents), for delicious pastries and coffee.

Italian market on Arthur Avenue, New York CityChris Goldberg/Flickr

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