All I can assume, as I spot the closed doors of the Convent of St Nicholas in Trogir, Croatia, is that Kairos has flown off on holiday, since the building I want to visit is shut.

Kairos is the Greek god of an opportune moment (the irony isn't lost on me); according to mythology, if you don't seize him as he shoots by on his winged feet, your happy moment's past and your lucky chance, gone.

The town of Trogir, 20km west of Split on Croatia's Dalmatian coast, hosts a festival to honour the god every year. Its convent also has a famed bas-relief of him, carved out of orange marble in the 3rd century.

But it seems I'm not going to see it. I can, however, buy a "happy moment" ice cream from a local stall. A poster pinned above the price list depicts Kairos flying over icy mounds of branded peach gelato.

Luckily, Trogir's Old Town, set on an island and surrounded by medieval walls, has other attractions too.

I wander through its cobbled streets, explore the main square with its Romanesque-Gothic cathedral, and enjoy a traditional lunch of grilled sea bass and boiled potatoes, served with a glass of Croatian plavac mali, a wonderfully fruity red wine.

That afternoon, I visit Split, Croatia's second city. It's a tangle of Roman and medieval alleyways, born out of the ruins of Emperor Diocletian's palace built around 300 AD.

The enormous vaulted cellars, constructed largely to raise the emperor's living quarters above those of his subjects, are filled with stalls selling scarlet coral jewellery and natural sponge.

We cut through what was once the entrance to the royal apartments. Four men are performing klapa, a style of a cappella, typical of the region of Dalmatia; their voices echo round the chamber.

From Split, it's an hour's drive southeast to our hotel, Thomson's adult-only Sensimar Adriatic Beach, situated 20km south of the town of Makarska on the Makarska Riviera.

The four-star, all-inclusive Sensimar Adriatic, which sparkles after a recent refurbishment, seems to celebrate the sea; most rooms overlook it, as does the sweeping infinity pool, just down from the spa.

Every evening, the sun sets over the water in full view of the Mojito bar. I watch the tangerine ball slip slowly behind the headland with every sip of my cocktail.

On my final day, I'm up early. I cut through the hotel grounds to the shore and follow a trail along the shingle beach to the neighbouring village of Igrane, around 2km away.

Gradually, the Adriatic turns turquoise with the brightening sun. In the distance, the islands of Brac and Hvar glint across the water. Brac is known for its milky-coloured limestone which was used to build the White House; Hvar is often described as Croatia's St Tropez.

Later, I take a ferry from Drvenik, a 10-minute drive from Makarska, to Sucuraj on Hvar's eastern tip. It's a blustery 40-minute crossing under a brilliantly blue sky. Sucuraj lighthouse, with its square tower and terracotta tiled roof, heralds my arrival from a rocky peninsula.

Hvar island is long and thin, with olive groves and lavender fields either side of a steep, central ridge. In the south, vineyards produce the renowned plavac mali grape.

The main settlement, Hvar Town, lies below a colossal citadel whose crenellated walls straddle the hillside. The central square has a Venetian arsenal where war galleys were once repaired. At the eastern end is St Stephen's cathedral with its trefoil facade.

Stepped, cobbled streets lead off the plaza in all directions.

Down on the seafront, ferries offloading day trippers jostle for space among shiny super yachts. Celebrity visitors include Tom Cruise, Clint Eastwood, Keira Knightley and Prince Harry, who's said to have enjoyed an impromptu dip during a party at one of the nightclubs.

Beyonce's daughter, Blue Ivy, is even an honorary citizen, after the singer tweeted she named her baby after a beautiful, ivy-clad tree she spotted while on holiday.

We may not need to dodge the paparazzi ourselves, but that doesn't deter us from a celeb-style lunch. Towards the headland, in the direction of the Franciscan Monastery, is DiVino, with tables on a beautifully planted terrace.

Dishes include marinated octopus, sea bass and lamb crepinette. We sit overlooking the Pakleni islands as yachts cruise round the bay. It's chic, classy and away from the crowds; Kairos may have escaped me earlier, but I've now found my happy moment.

TRAVEL FACTS :: Karen Bowerman was a guest of Thomson (thomson.co.uk; 0871 230 2555) who offer seven-night holidays to Croatia staying at Thomson's Sensimar Adriatic Beach on an all-inclusive basis from £895pp (two sharing). Price includes flights from Gatwick and transfers. Package add-ons include excursions to Hvar (£62pp) and to Trogir & Split (£35pp)