When I get there, Thierry, the textile manufacturer from Lyon, is already sitting at the bunkhouse table with his wife, Anne, someone big in affordable lingerie. They're talking to Jerry, formerly of the Rhodesian police, who departed hastily from both job and country just before Robert Mugabe moved in. Jerry's young South African wife, Salome, enjoys winding up the French couple by talking about M Hollande. "Frankly, I'm amazed you know the name of Valerie Trierweiler," says Anne, sniffily. "She has never been an important person." Salome smiles.
Taking their seats for lunch are Ed and Sam, a gay American couple, plus their Norwegian pal, Tomas, and his foxy girlfriend, Gretel. Beside me, Alfred, the Swiss doctor, tells the company that, after completing his national service, he was given the option of keeping his Glock pistol and has it at home. Jerry confirms the importance of keeping a gun in the family living-room, when you're in the Jo'Burg suburbs, post-Mandela. Gretchen, a tall and domineering engineer from Bremen, narrows her eyes at the nice doctor.
Where is this 12-strong League of Nations gathered alfresco round a table in the middle of nowhere? Welcome to La Bamba de Areco, an estancia in the pampas, 90 minutes' drive north-west of Buenos Aires. This is where adventurous visitors finish off their tour of Argentina; Thierry and Anne and Alfred and Grechen and Ed and Sam and the others have taken in the main sights in their two-week stay; they've gawped at Iguazu Falls on the Brazil border or the Itaipu dam on the Brazil/Paraguay border, they've flown to Mendoza, the wine region by the Andes, or the southern fjords in Patagonia, and they've stayed a couple of nights in BA.
The 'real' Argentina: A league of nations
The 'real' Argentina: A league of nations
Market in Plaza Dorrego
Argentine tourist board
Puente de la Mujer in Puerto Madero
Argentine tourist board
A place in the country: riding out from La Bamba de Areco
Inside the estancia
Argentine tourist board
Plaza de Mayo, Buenos Aires
Argentinian Tourist Board
La Bamba is the crash-out zone for the weary traveller en route home. At every lunch we're served a dozen courses: rocket with cheese, tomatoes, courgettes, sausage, chicken, pork and beef, then pancakes of dulce de leche, that ubiquitous, tooth-rotting Argentinian favourite, the pancakes seared with a branding-iron from the 10ft-long parilla grill – all of it washed down by cold Alamos malbec.
For the guests, this place is a haven, a departure lounge, a decompression chamber for tourists saturated with Argentina's massiveness, its mongrel culture. It was built in 1830 as a resting-place for weary travellers en route from Peru to Buenos Aires. The stagecoach would be housed in the pulperia, or barn, now the restaurant; ladies slept by the huge log fire, while the gauchos kept watch outside with their ponchos and long knives.
In the 1940s the Aldaos family bought the place as a working ranch – and since 2010, it's been a luxurious estancia (ranch) hotel, operating year-round. The owner is a French businessman, Jean-Francois Decaux, whose wife, Pascal, has designed it, equal parts cool and luxurious. The rust-and-cream exterior is traditional; the rust colour is a mix of red paint and pig's blood. Inside it's all polo chic: dark wood, teak and mahogany, lots of silver, mirrors, dark statues and horsey pictures. Each guest couple have their own beautifully upholstered shack. There are 11 shacks in all, full of coffee-table books, with photos of polo teams, all of whom look like boy bands.
You can visit the outdoor pool or take one of the 60 on-site polo ponies for a trot, or watch one of the gauchos perform a romantic horizontal ballet with his horse. Or you can sit on the porch and reflect on your visit to Buenos Aires, and how hard it was to identify the "real" BA – or indeed the "real" Argentina – in its busy streets.
Like London and Manhattan, the capital is a city with scores of district neighbourhoods or barrios (48, to be precise) each one with (you're told) its distinctive character. But unlike London's Soho and Chinatown, or New York's Little Italy or Meatpacking District, BA's districts tend to bleed into each other. They all have boulevards and buildings, shopping galerias, squares and gardens that remind you of other places. Puerto Madero, the bustling and expensive reclaimed-dock areas, where we stayed in the friendly and chic Madero Hotel, is basically Canary Wharf. In the Microcentro, the Plaza de Mayo is essentially Hyde Park Corner, but with equestrian statues and palm trees.
The majestic avenues of the banking district remind you of Haussmann's boulevards in Paris with their black cupolas, wrought-iron balconies and air of solemn grandeur. The Calle Florida, once the city's most elegant retail mall, is pedestrianised and Soho-ish: there's even a branch of Harrods, tragically shut since the 1960s.
Palermo, the largest of the city's 48 barrios, has a sheen of dazzling trendiness, especially the section called Palermo Soho. The streets are tree-lined and every intersection features cutely designed shops and bars. It's a young neighbourhood: here a pour la maison shop with a courtyard café; there a tiny emporium of Jesus Fernandez knickers. Then, there's La Cabrera, the best steakhouse in BA, where the steaks are 800-gram monsters of nubbly, meaty bliss, accessorised by 40 mini-plates of chimichurri and spicy pulses. There are scores of independent clothing shops called things like Bokura and Etiqueta Negra, with fashionably sneery assistants, and cool, if pricey, shirts.
At every turn, you're confronted by things that remind you of Manhattan, Paris, London, Milan and Barcelona. So, where do you find the taste and smell and feel of authentic Buenos Aires?
The most characterful barrio is San Telmo, where rich landowners built themselves palatial houses in the 19th century. After an outbreak of yellow fever in 1871, the gentry legged it further north to Retiro, abandoning their mansions. Canny landlords turned them into tenements crammed with immigrants.
On Sunday afternoons, the antiques market swings into the Plaza Dorrego, offering bijoux made of rhodochrosite or Incan Rose, the baby-pink semi-precious stones unique to Argentina; and displays of gaucho paraphernalia. It's nice but feels a little fake and tokenish, just as La Brigada, the restaurant to which you're directed by the hotel concierge, a place festooned with football shirts in glass cases, isn't really the authentico vibe you're looking for. (We found that at Bar El Federal at Carlos Calvo 599, one of the oldest bars in town, with elaborate wood carvings, snugness and an ancient mangle on the wall.)
Ask the locals for the most typically Argentine of sights and they'll direct you to Recoleta, the city's most elegant neighbourhood. It's the home of the National Art Gallery, Design Museum and National Library, but they're not the real point. The point of Recoleta is the dead, the inhabitants of the Cementerio, where Buenos Aires's poshest families honoured their ancestors. Each grave is attended by more statuary, crosses, candlesticks and caryatids than the last. This crazy ostentation is less about celebrating the dead than demonstrating each family's vanity. Crowds gather at the flower-strewn door of the Família Duarte, the burial place of one Eva Perón. So, that's authentic. It's just a little oppressive and melancholy.
It was a relief to leave the capital for the pampas lands, where men are men. The gauchos we met were from the cool end of the spectrum with their red neckerchiefs and black berets. Their saddles were upholstered with sheepskin rugs, and their holsters contained nothing more dangerous than mobile phones.
Nothing though, prepared me for the trip to nearby San Antonio de Areco. It's known as one of the best-preserved Argentine towns and the home of gaucho culture. But no guidebook tells you about the history the way Magdalena Ramirez tells you. As she rattles you into town in a bucking 4x4, she claims to be able to tailor her official-guide strategy to whichever nationality she's talking to. When I told her my family background was Irish, she swerved wildly. "Just you wait!" she said.
The 4x4 slewed into San Antonio, an ordinary looking town of dusty pavements and little shops, which gave way to an impressive central square, the 18th-century Plaza Ruiz de Arellano, with its simple but charming Church of San Antonio de Padua. "No, you must come and look," said Magda, as I suggested we got out for a walk. "Look at what?" I asked. "You'll see," she said and zoomed through some winding streets before stopping dead outside another white church. She said nothing, only pointed at the statue above the pediment.
I got out and looked. Mother of God. It was Saint Patrick, patron saint of Ireland. There were even a few Hibernian snakes under his feet.
Inside, the walls were hung with the 14 Stations of the Cross. There was an Irish tricolour in the lady chapel and a brass plate in the floor announced that the Right Reverent Monsignor Richard J Gearty (1863 – 1938) was Irish Chaplain of San Antonio for 35 years from 1902. The citation called him "Our soggarth aroon" Irish for "dear priest".
"Many Irish came to Argentina during the Famine," explained Magda, "the late 1840s and 1850s. There were Irish nuns, Sisters of Mercy, priests and families with nowhere to live. In the 1870s, an outbreak of yellow fever devastated Buenos Aires. The Irish immigrants, especially the nuns and priests, helped the stricken porteños – locals from Buenos Aires – after which the community was accepted. They were given 60 acres and permission to build a hospital, schools, residences."
It was like discovering what happened to your ancestors. My Galway father's ancestral neighbours, the Duggans of Mayo, turn out to have a ranch 15km from San Antonio, and are known as producers of the best Hereford cattle for miles. There's even a town called Duggan.
Back at the estancia, I reflected that a single morning in San Antonio had brought me closer to discovering the authentic Argentina than four days in the capital. Because this is a country pullulating with immigrant cultures that have come for a new life and, like the Famine-fleeing Irish, broadly flourished. Maybe the key to Argentina is the simplicity of its lines, its great fields, its huge horizons, its meaty cuisine, its Catholic culture – it's a great green canvas, on which many lucky blow-ins from Europe have come and made their mark.
As I'm sure Thierry and Anne, Jerry and Salome, Ed and Sam, Alfred, Jerry and Gretchen and all the other multinational travellers, now heading like sated cattle into dinner at La Bamba's elegant, candlelit dining-room, would agree.
John Walsh travelled with Bales Worldwide (0844 488 0663; balesworldwide.com), which offers eight-day trips to Argentina from £2,995pp including flights from Heathrow, accommodation, some meals, transportation, sightseeing and tango lessons.
The only non-stop flights from the UK to Argentina are on British Airways (0843 493 0787; ba.com) from Heathrow to Buenos Aires.
John Walsh was a guest at La Bamba de Areco (00 54 11 4519 4996; labambadeareco.com) where doubles start from US$580 (£387) per night, full board. Guests can also reserve the entire estancia for private gatherings from US$6,620 (£4,413) per night.