The best-laid plans for an arty outing to Venice will never come exactly to fruition. You optimistically annotate the map for the Bellini altarpieces, Veronese ceilings and Titian portraits. You clutch the flyers for candelit Vivaldi in evocative churches, and you plan your morning assault on the Ducal Palace with all the cunning of a medieval Doge.

Then you arrive in a sweltering La Serenissima and realise what Venice is actually about: an enormous game of hide and seek. The strategy changes from hunting Renaissance jewels to finding secluded bolt-holes and canalside trattorie with free tables, while just around the corner lurk the faceless blob of tour parties heading in your direction.

The weight of people traffic between the Rialto and St Mark’s Square is almost enough to make you give up altogether. But even when you are beached in St Mark’s Square, and the crush has never seemed so dispiriting, salvation can be just one boat ride away.

In fact, the only way to venture on to San Giorgio Maggiore, the island whose majestic church gazes serenely out at the chaos opposite, is to hop on a vaporetto from St Mark’s on a route south, to Palladio’s masterpiece, the church that gives San Giorgio its name, and then on to the narrow spine of land known as the Giudecca.

There is even more reason to visit San Giorgio Maggiore this year with the eagerly awaited refurbishment of Teatro Verde, an open-air theatre promising top-class opera and ballet productions. The theatre is surrounded by cypresses, and tucked away on the south side of the island. Unfortunately, the opening has been beset by financial problems so no music sounds in San Giorgio just yet.

Still, silence aside, a visit here is essential for the claustrophobic culture-vulture. Considering just how many painterly views of Venice include a dramatic view of San Giorgio Maggiore (a wonderfully misty, but not exactly unusual, specimen by Turner recently sold at Sotheby’s for almost £3 million), the number of people who actually turn up for a closer inspection is surprisingly small.

Hotels will sell themselves on the view of the island, but not many will tell you to go there. And once they’ve paid their fare for the three-minute ride and stepped on to this tiny island – home only to eight monks – most visitors are to be found huddled on the church square taking snaps of the Venice they have just escaped.

Palladio’s design deserves more attention. To create the gleaming white edifice of San Giorgio, he cannily slapped two Greek temple styles together. It should be a jarring mess, but it brims with neo-classical confidence, and the whole makes for a wonderfully pure antidote to the Byzantine bling of St Mark’s Basilica.

Inside the coolly harmonious interior lies the closest thing to an artistic secret that Venice has to offer. Tintoretto’s luminous colours have never looked as alluring as they do in his late, great Last Supper, which he filled with lively incidental detail. Just beyond are the intricate wooden choir stalls of the Flemish master, Alberto van Den Brulle, illustrating 82 episodes of the life of St Benedict.

After this double-whammy, recover by climbing the church campanile (there is a monk-operated lift) for a view that is both less expensive than St Mark’s belltower and has a more breathtaking panorama.

That used to be all that San Giorgio could offer, but the charity that owns the island, the Cini Foundation, is finally making more of its assets. Guided tours are now offered to the monastery buildings, which include two beautiful 17th-century cloisters, a library with illuminated manuscripts and rare Vivaldi scores, and a refectory. The island now has its first café, which sits by the marina facing St Mark’s and makes up in location what it lacks in atmosphere.

Whether you’ll get to visit the remaining jewel in San Giorgio’s crown – Teatro Verde – is still unclear. Earlier this year, a cartoonish production of a Strauss operetta presented by a German consortium folded within weeks of opening; now the foundation is promising more serious opera and ballet for the autumn nights.

You have two choices when leaving San Giorgio: chug back to the maw of St Mark’s or stay intrepid and continue on to the quiet streets of the Giudecca. You’ll find another Palladio (the brighter, but less subtle, Redentore) and, after a short hike through a boatyard, the airy and well-priced restaurant, La Mistra. Here you can enjoy a hazy view of the Lido, and jostle with company made up largely of loud and thirsty shipwrights. Back on the well-worn paths, you’ll thank yourself for this native intermezzo. Information on productions at Teatro Verde: www.teatroverde.eu.

Need to know
Neil Fisher stayed at the Hotel Cipriani (020-7960 0500, www.hotelcipriani.com), which is open until November 18. A standard double room costs from £437 a night, including breakfast.

A night at the open-air opera

Construction of the open-air Teatro Verde began in 1952. It took two years to build the stage and stepped stone rows, which can seat up to 1,400 spectators. The overall look was elegant, but functional: a classical amphitheatre recast in sober 1950s modernism, but surrounded by lush vegetation and secluded both from “mainland” Venice and the adjacent monastery. Each row is separated from the next by privet hedges, providing the greenery that gives the theatre its name.

In the early years performances took in anything from La Scala ballet to Baroque opera, Greek tragedy to commedia dell’arte, but by the 1970s the theatre had largely fallen into disrepair. It was only in 1999 that the foundation made the first moves to restoring the theatre. The latest refurbishment finished this spring after a private consortium was put together in 2006 with the intention of producing a summer season of opera performances.

Modern stage machinery was installed, dressing rooms and foyers were completely refurbished, and the rows of seating given a thorough spring-clean – without disturbing the utilitarian ambience.

The theatre’s new guardians are aiming for a series of performances in September after an aborted production of Strauss’s operetta One Night in Venice, which closed in May a few weeks after opening.