The search for optimum health means I’m not a regular drinker of alcohol. But there are two drinks I find hard to resist – a martini with a twist in a New York bar, and a Bellini in Venice.

Martinis can pack a punch and Bellinis provide a pleasant hit of dopamine. But it’s not about the alcohol content or even the taste of the drink.

It’s about the sense of place.

In Venice, you’re automatically offered a Bellini or an Aperol Spritz when you sit down for a drink at a restaurant or bar. Both are specific to the city.

The spritz was created in the early 19th century for Austrian soldiers stationed in the Veneto region who liked a splash of water added to their wine.

Get exclusive travel deals delivered straight to your inbox. Sign up now.

When Australians put ice cubes in their white wine, it’s a similar concept, as much as the French seem to deplore it.

I can’t stand the bitterness of Aperol, so my go-to summer evening cocktail in Venice is the Bellini. It feels like the most romantic drink in the world when you’re sitting on a rooftop terrace watching the sky turn apricot and pink.

Unfortunately, the tourist version of the Bellini is often an over-sweet, pink-hued concoction made of peach syrup and low-quality prosecco, not the fresh peach it requires.

You’d expect better in Venice, but most bars in well-trodden spots cater to the sweet palates of American tourists.

Most visitors don’t care or notice if the Bellini isn’t made with fresh peach.

But I think there’s something wrong if you’re served the same sickly drink they serve at hens’ parties back home.

On my last trip to Venice, I tried to figure out what the perfect Bellini might be. The starting point in this pilgrimage is Harry’s Bar, tucked away on a narrow street near St Mark’s Square.

It was opened in 1931 by bartender Giuseppe Cipriani, who went on to establish one of Venice’s finest hotels, The Cipriani, and invented the dish carpaccio along the way.

The cosy bar is a designated Italian National Monument, and is most famous for being the place where Ernest Hemingway liked to drink – and for the Bellini, which Cipriani invented in 1948, naming it for the Renaissance painter, Giovanni Bellini.

I had never been there until this year when friends, visiting from Melbourne, invited me for a drink. I’d avoided it because I heard it was touristy.

And it is. But it was fun to be somewhere so steeped in history, even though the legendary Bellini was a bit of a disappointment. It may have been made from real peach, but it was made in such volumes it didn’t taste hand-crafted. A small glass sets you back about €22 ($36) at the bar.

For those who think the Bellini is a woman’s drink – Hemingway apparently drank both martinis and Bellinis at Harry’s.

Across the water at the Hotel Cipriani, A Belmond Hotel, on Giudecca Island, Gianfranco of the hotel’s Bar Gabbiano makes a Bellini for me using fresh peaches.

The white peaches from the north are best, he says, the juice often hand-squeezed. Gianfranco pours the fresh puree into a special glass jug, then tops it with prosecco, waiting until the froth settles before adding more peach.

One part peach to two parts prosecco is the approximate recipe, although Gianfranco says it’s a bit like cooking, the proportions can be varied to taste. It’s elegant and not too sweet and all the better for being served poolside by the lagoon.

To my surprise, another excellent Bellini I tasted in Venice didn’t have Cipriani associated with it.

Hotel Heurekais a charming, independent hotel in untouristy Cannaregio. A small palazzo of 10 guest rooms, it has a beautiful private garden and an intimate bar in the lobby, where Alessandro, who spent 34 years as bartender at the now-closed Bauer Hotel, presides.

One evening, he was making a jug of Bellinis for two other guests, so I joined in. It couldn’t have been fresher. He pureed the juicy peaches on the spot and topped them up with a medium-dry prosecco. It was perfection, fruity but barely sweet at all.

You could, if you liked, buy a “peach-flavoured” Cipriani Bellini at a bottle shop in Australia for about $30.

But a true Bellini needs to be enjoyed in summer in Venice, its place of invention, when the peaches are ripe.

Everything else is a sugary cocktail.

The writer was a guest of Hotel Heureka and the Hotel Cipriani.