A perfect way to get your bearings is by joining our ‘orientation tour’, which includes a visit to the Observation Deck on the 86th floor of the Petronas Towers, the capital’s most iconic buildings. More historic character is to be found in the old colonial quarter across town, where the intricate, Moorish-style Jamek Mosque is the standout building. To its south, Chinatown’s shophouses, traditional cafés and colourful Buddhist temples give a sense of what KL might have been like half a century ago. The superb Islamic Arts Museum, whose ultra-modern premises is crowned by a turquoise-tiled Persian dome, is another of the city’s key sights.

Encompassing 4,323-square-kilometres of primary rainforest, rivers and cloud-fringed mountains, Taman Negara is the country’s top national park. Its few remaining large mammals, which include elephants, leopards and rhinos, are rarely sighted these days, but it’s still worth the trip to experience the jungle in the raw: the cacophony of insect and bird noise is a revelation.

A superb canopy walk suspended 30m above the forest floor makes for an adrenalin-fuelled introduction to Taman Negara, while rides on wooden longboats take visitors deeper into the park to waterfalls, caves and the start of longer trails. Orang Asli villages where visitors are invited to try their hand at blowpipe hunting and fire making are other attractions.

On the eastern flank of the city facing the South China Sea, Telu Chempedak (aka ‘Palm Beach’) is a gracefully curved bay backed by casuarinas and pines. Kuantan-ites enjoy escaping here on weekends for a dip and a meal by the waves. The barbeque srestaurants behind it serve succulent local seafood and spicy satay.

After breakfast, drive up the coast to Cherating, an arc of coarse, golden sand that’s protected as a nesting site for marine turtles. In the village behind it under the casuarinas, you can try your hand at traditional Malaysian batik, and visit a workshop where beautifully soft mats and baskets are woven from bamboo and dried pandanus leaves. This is also a good place to watch local in-shore fishing in action: the catch is landed each morning by water buffalo! After lunch, visit a striking black-sand beach near Cherating before returning to Kuantan, where you’ll call at the city’s principal mosque and Hindu temple before returning to your hotel for supper.

Riding high on revenue from the region’s recent oil boom, go-ahead Kuala Terengganu is the capital of a region that’s nevertheless still predominantly rural and traditional. Its bustling street markets, old town, boatyard and a particularly good museum make it a commendable base from which to visit the Yak Yah Firefly Sanctuary at Kampung Ibok, further up the coast, where you’ll spend the evening. After a picnic supper next to the beach, climb aboard a silent, electrically powered sampan for the cruise upriver to the largest conflagration of fireflies in the Malaysia – a spellbinding spectacle.

A gleaming pile of steel and glass, Terengganu’s ‘Crystal Mosque’ is a strikingly exotic spectacle and the obvious place to start any city tour. Afterwards, explore the atmospheric streets of Chinatown before visiting the State Museum, with its exceptional collection of antique textiles and Koranic calligraphy. In the afternoon, relax back at your hotel or jump on a ferry for a stroll around the harbour on Pulau Duyong, an island at the mouth of the river, which retains a picturesque Malay fishing village and yard where wooden boats are still made by hand.

Twin jewels of the Teregganan coast, the Perhentian Islands are both archetypal tropical paradises. Kecil is the least developed of the pair, and our preferred option thanks to its superior diving facilities. In transluscent, turquoise sea, you’ll snorkel with turtles and dive in shoals of colourful fish. Winding paths through jungle filled with exotic birds connect the two beaches: ‘Long Beach’ and ‘Coral Bay’. Evenings tend to be spent at a restaurant gazing at the fabulous sunsets and marvelling at the starry skies.