Does it have any rabbits?

Our four-year-old son’s summer season opened in May this year, with a line of dancers wearing black leotards, black sunglasses and Perspex sonic tutus, moving in a long line up the steps of an office building near Wall Street.

His two-year-old sister was a little taken aback by the steady electronic roar and the high-pitched amplified audio crashes that erupted when the dancers struck out and dragged the garden rakes they were carrying against the concrete.

But not the boy, Ivan. He knows art when he sees it. Afterwards, he cornered one of the dancers from Die Audio Gruppe, a Berlin-based sonic performance group, and quizzed her about the wires and boxes and batteries fixed on to her plastic tutu.

“That? Oh that’s a light-sensitive electronic switch.”

After three summers in Manhattan, Ivan has pretty much worked out that anything weird or unusual in the open air is Art, and could be cool. Scores of dancers rolling like logs down the grandiose steps of the New York Public Library on Fifth Avenue on a hot afternoon? Art. Performers dressed in 1940s trench coats running up and down an Essex Street garage, in front of an audience sitting in parked cars? Art.

For Manhattan in the summer, with its wealth of open-air concerts, dance performances and, well, Art, is the Uberkunstkindergarten, providing relief and entertainment both to surprisingly small children and to their parents, and all - by and large - without annoying the rest of the audience.

Site specific? Open air? Count us in. Cities - especially New York - are noisy places and can cope with a few questions or an occasional squeal from a baby sling. In the event of things taking a turn for the worse, you can always just walk away and go home, because it is nearly all free - and unlike drama, you don’t always need to know how it ends.

So Ivan has scampered through Christo and Jeanne-Claude’s The Gates project in Central Park, and gazed on the late Robert Smithson’s strange Floating Island on the Hudson river, a barge landscaped with trees, grass and flowers and pulled by a tugboat (”Does it have rabbits?”).

And sometimes he brings a unique perspective - for instance to last year’s open-air gathering of 50 different New York artists on Governors Island in New York Harbour, five minutes by ferry from the tip of Manhattan. As the city ponders what to do about the former coastguard base, it handed over the island’s green meadows to The Muster, a project by Allison Smith based on the pressing contemporary question “What are you fighting for?” We liked Knitting Nation, an installation involving a woman in a dress of red, white and blue, declaiming from studies and tracts on the history of industrial knitting and war, while an adjacent sweatshop toiled away on a giant American flag. Ivan particularly liked the guns - even if they were purple wooden ones which the young men holding them called “love guns”. And he liked the Civil War-style first-aid tent guarded by ghoulish soldiers and entitled “The Right to be Scared”.

Sadly, Ivan has occasionally not managed to keep up with the agenda. We may have overdone it with Picture Red Hook, a spectacular piece enacted on a 12-storey wall of disused grain silos in the old Brooklyn port of Red Hook, which included extensive use of synchronised abseiling and dancers suspended and winched across the abyss by a construction crane. Being just over a year old at the time, Ivan fell asleep in his stroller.

He can also serve as a critical canary in the artistic coal mine. Last year, Noemie Lafrance, an artist whose annual site-specific events are always ambitious, launched a piece called Agora in the vast, disused McCarren Park swimming pool in Brooklyn’s hip Williamsburg area, with hundreds of people in the audience perched around the edge while 30 or more performers did various things in the old pool basin.

According to the programme, Agora’s overlapping narratives were supposed to “produce the illusion of travel through the different layers of visceral urban experiences and explore the phenomenon of agoraphobia as a social and physical reaction to urban architecture”.

It didn’t really work - despite the presence of members of one of our favourites, the Streb Laboratory For Action Mechanics (Slam), who were performing some of their signature body-slamming moves in an inflated pool that had been laboriously filled by a procession of water-bearers. But 50,000 square feet requires North Korean-style choreographic intent to make a significant impact - a verdict underlined by the fidget-ometer reading on the somewhat perplexed offspring, who generally likes his waterborne body-slamming art event up-close enough to get splashed.

A year earlier, though, Lafrance’s Noir - the parking-garage event - had had him on the edge of his car seat in our family station wagon, while his six-month-old sister gurgled in the front seat. “Where’s she going?” “Why is there a bicycle?” - exactly the questions that should be posed by a work billed as “tracing the evolution of suspense in narrative through the language of choreography”.

Tom Johnson, a sculptor and performance artist who lives in Brooklyn, has seen things from the other side. Last year, Tom, a friend of ours, spent several hours every week performing The Standing Post, which involved sitting with just his head exposed in an aluminium box outside the Museum of Modern Art’s PS1 in Queens, one of the leading New York contemporary art spaces. There, and over a three-month run in Turin, he met his share of children, many concerned, since his body was hidden, about whether he had any clothes on.

“It’s good for children,” he says, “because there’s a tradition in performance art that has to do with asking questions - very simple questions - about being a person in front of other people. Those are questions that kids deal with an enormous amount, especially if they’re going to school for the first time. Plus it makes them think. And that’s good for grown-ups too.”

So we’re all ready for the peak of the summer season this month. There’s the River to River Festival downtown, and the weekly Summer Stage performances in Central Park - which last year gave Ivan valuable exposure to the talents of Patti Smith (”Too loud for my ears”). Sadly, we had to give up on waiting for the late appearance of the British/Sri Lankan rapper MIA and DJ Rehka, our appetite for bhangra rap worn down by the relentless preceding barrage of high-volume “reggaeton”.

And there will be the latest offering from Dancing in the Streets, the institution that arranged to roll dancers down the steps of the Public Library and hoisted them in the air over Red Hook. This year will see the second of its dance “charrettes” - in which a group of choreographers are given just five days to develop a dance for a previously unknown site. Did someone say site-specific? Bring the family.

Jonathan Birchall is an FT correspondent in New York.