Travel: City Island, New York.

It's the city that never sleeps so, in theory, it's the perfect place to take a baby. In theory. Sitting on the floor at home, surrounded by tiny outfits, piles of nappies, toys, a pushchair, a car seat and numerous other "just-in-case" items, we suddenly doubt the wisdom of our brilliant plan to introduce our son to the pleasures of New York City.

Fast forward a few hours and everything is looking brighter. The United Airlines staff whisk us on to the plane, settle us in our seats and spend the flight fussing over our first-time flier. And despite the fearful looks of our fellow passengers, the youngest traveller on the plane gently snores his way over the north Atlantic all the way from Edinburgh to Newark Liberty airport.

Having lived in New York for years, we have already visited the major landmarks, so this time around we've decided to get off the beaten track and explore another side of the city. Bypassing the Empire State Building, the Statue of Liberty, Central Park and the crowds that go with them, we head instead to the Bronx and City Island.

Many New Yorkers live their whole lives in the city and have no idea this beautiful little island exists. Measuring one-and-a-half miles by half-a-mile, City Island is home to 4000 people. Some families have lived here for generations and are enormously proud of their little corner of New York. Looking around, at the neat rows of pretty pastel-coloured clapperboard houses, tidy lawns and picture-perfect seafront, it's not hard to see why. City Island couldn't be more of a contrast to the skyscrapers and thronging streets of Manhattan, little more than an hour away by bus and subway.

Created by glacial deposits at the end of the last Ice Age, it looks and feels like a New England fishing village. With the sound of the water lapping the shoreline, life here progresses at a sea snail's pace. The pavements are empty except for a handful of locals, making it a great place to stroll with a little one. A browse in the antique shops dotted along City Island Avenue throws up some interesting flotsam and jetsam, from an old ship's wheel to art deco jewellery. But the price-tags are beyond us and we don't fancy our chances haggling with the tough-talking lady behind the counter who's speaking non-stop on the phone while filing her nails.

We leave empty-handed and head to the Nautical Museum to learn more about the island's history. Perched high in a tree outside the museum is a bright-green parrot, one of City Island's unofficial mascots. Known as monk parakeets, they were originally brought in to the area from South America as pets but over the decades have adapted to the climate and started to breed in the wild. This one gives a loud shriek as we pass, to the delight of our baby. Inside the museum, maps, paintings, photographs, models and artefacts bring the area's seafaring past to life.

Volunteer guide Mike explains that the island's name dates back to the late 18th century when a Benjamin Palmer bought it with the intention of transforming it into a port city to rival Manhattan. The American Revolution put paid to his vision, depleting his capital and that of his investors. But over the decades a community of oyster-fishers and shipbuilders settled and thrived and New City Island became simply City Island. During the First and Second World Wars, it produced minesweepers, tugboats and landing craft. In the post-war years, the focus switched to boatbuilding, with the island producing seven America's Cup-winning yachts. To this day, this largely blue-collar town is home to several yacht clubs, the focus of a lively social scene.

A black-and-white photograph on the wall of the museum shows a group of 20-somethings in their Sunday best gathered on the beach for a picnic in the 1940s. In another, a group of glum-looking children, brushed and polished to within an inch of their lives, takes a trip on a monorail, accompanied by a stern-faced nanny. Back then, Manhattan, with its neon lights and towering buildings, must have seemed a lifetime away. The fashions of the mainland would take years to arrive here, if they ever did, and older residents recall visiting relatives in Manhattan during the holidays, then considered a major undertaking.

Nowadays it can be reached by car or pubic transport via a free bridge, but City Island retains its old-fashioned small-town atmosphere. It can get busy during the summer months, making a visit off-season or during the week the best way to get a glimpse of a way of life which has all but disappeared in other parts of the country.

With its own firehouse, library, school, post office and general store, the island is a self-contained community. It even has its own newspaper although there's only enough news to fill 10 issues every year. Many of today's City Islanders travel to the mainland for work but there are still residents who boast that they never leave the island and eye their big city neighbours with suspicion. They include Jesse, a retired fisherman who has stopped by the museum today to chew the fat with the volunteers. "We have a lovely quiet life and a big beautiful house two minutes from the water. Why would we want to leave?" he asks. He last took the bus to Manhattan years ago to renew his driving licence and has no intention of going back. He tells us the island is divided into mussel-suckers – residents who come from somewhere else – and clam-diggers, born and bred on City Island, often in a house handed down for generations.

We leave the museum and hop on to a trolley bus with strict instructions to seek out lobster, a local speciality. Giving the pricey-looking restaurants along the seafront a miss, we visit a seafood shack down by the water instead. With a handful of seagulls for company, we chow down on lobster rolls and watch the waves rolling in. Just along the waterfront, a tangle of fishing nets glistens in the sun. The fishermen came back with their catch early this morning, just as generations did before them.

Many of the grandest mansions on the island owe their existence to fishing. Back on City Island Avenue, the Samuel Pell Mansion, the former home of one of the area's leading oystermen, stands out among the Victorian mansions with their towering spires and ornate wooden gables. It was here that the 1944 comedy Arsenic And Old Lace was filmed, starring Cary Grant as a man who learns on his wedding day that his aunts are homicidal maniacs. Fans of the film will recognise the three-storey Victorian house which was home to the maiden aunts and still has much of the original ornamental woodwork.

With its beautiful sunsets, gorgeous architecture and picturesque street and beach scenes, the island is well known as a movie location, and has also featured in A Long Day's Journey Into Night (1962), The Royal Tenenbaums (2001) and Margot At The Wedding (2007). But it took until the 2009 movie, City Island, for the location to feature as itself instead of doubling for an anonymous New England fishing village.

Even City Island's New Yorker director, Raymond De Felitta, had never heard of the place until he discovered an article about it in the travel pages of the New York Times while looking for locations: "It's not unusual for New Yorkers not to know City Island. It's very strange. It's a very unexpected, private little spot, with fishing villas facing the most famous skyline in the world, I just loved that. It was a gift of a setting."

The movies may have fallen in love with City Island but they've done nothing to dent its charm, which is on ample display when you take a garrulous baby around in a pushchair, sorry, stroller. City Island may not have the skyscrapers but it combines the most terrific view of the big city with an old-world charm of its own.

TRAVEL NOTES

GETTING THERE

United Airlines has return flights from Edinburgh to its New York hub, Newark Liberty, from £481. Visit www.unitedairlines.co.uk or www.continental.com. From Newark take the train to New York Penn Station. From midtown Manhattan, take the 6 subway train north to Pelham Bay Park then catch either the Bx29 or the BxM7A bus to City Island.

MORE INFORMATION

The City Island Historical Society And Nautical Museum is at 190 Fordham Street. Visit www.cityisland museum.org or call 718 885 0008.