For unspoilt wilderness: Sumatra
Sumatra is a naturalist’s dream, home to innumerable creatures that exist nowhere else on earth. Sadly it also represents the last – and probably fast-disappearing – opportunity to see many of them. The Sumatran tiger is scattered across the island, and Kerinci Seblat National Park offers the best (though still slim) chance of seeing it before it goes the way of its extinct Balinese and Javan relatives.
Other critically endangered inhabitants include the Sumatran elephant, Sumatran rhinoceros and Rafflesia arnoldii, the largest flower on Earth, whose putrid stench has earned it the nickname "corpse flower".
For jungle adventures: Kalimantan
Kalimantan, the Indonesian lion’s share of the huge island of Borneo, promises wild adventure like nowhere else in Southeast Asia. Borneo is the only home of the critically endangered Bornean orangutan, and Tanjung Puting National Park offers unrivalled opportunities to see these "people of the forest" up close.
You’ll take a cruise on a traditional klotok riverboat, an impossibly romantic way to make your way through the jungle, stopping off at feeding stations and viewing platforms. While the orangutans are the stars here, they’re joined by an impressive supporting cast of clouded leopards, long-snouted gharial crocodiles and gibbons.
Of Indonesia’s thousands of islands, few are as beautiful as the Togians, 56 perfect dots of rock, beach and jungle rising from the Gulf of Tomini in central Sulawesi. It’s not easy to get there – a good three days on buses and ferries from Tana Toraja – but determined travellers will get their reward.
The diving is first-class, with a sociable scene on the island of Kadidiri, and the snorkelling’s pretty spectacular too. At Jellyfish Lake, you can enjoy the therapeutic, if counter-intuitive, experience of swimming with thousands of non-stinging jellies, while the volcanic island of Una-Una makes for a picturesque day trip.
For world-beating diving: Raja Ampat
Indonesia has no shortage of world-class dive sites, and the likes of Crystal Bay and Tulamben are a big draw for many visitors to Bali. The best of all, though, lie way off the beaten track: the islands of Raja Ampat, off the coast of Papua.
With pristine coral reefs home to thousands of fish species, this is the most biodiverse marine environment in the world, and you’ll spot kaleidoscopic nudibranchs, huge manta rays and "walking" epaulette sharks, among many others. It’s still largely free of the crowds, but tourists are very well catered for, with plenty of dive resorts and liveaboards.
For ancient ruins: Java
Most tourists make only a passing visit to Java, the most populous island on the planet, in the form of a stopover in the polluted smog-bowl that is the capital, Jakarta. However, further to the east lie some truly remarkable ancient treasures.
Chief among them is Borobudur, the largest Buddhist monument in the world, which was covered by thick jungle until the nineteenth century – it’s 1200 years old, but it looks brand new. A similarly remarkable Hindu temple complex, Prambanan, lies nearby.
Few creatures exert such a grip on the Western imagination as the fabled Komodo dragon. The world’s largest lizard has been the subject of many myths since Dutch colonisers sent tales of "land crocodiles" back to Europe in the early twentieth century.
Up to 3m long and 80kg in weight, their toxic bite can fell prey as large as water buffalo, with the dragons stalking their victims for weeks as they slowly die. They live only on a small group of islands off Flores, easily reachable from the charming port town of Labuanbajo.
The spectacular highlands of South Sulawesi are a picture of serenity: water buffalo graze and goldfish bob in tumbling rice paddies, overlooking colourful villages with soaring horn-shaped roofs. It’s somewhat surprising, then, to learn that this is a land obsessed with death.
Most Torajans are nominally Christians, but their long-held animist traditions abide, centred around elaborate funeral rites in which hundreds of pigs and buffalo are sacrificed over several days. Foreign visitors can attend these ceremonies that, though graphic, are a vital part of Torajan tradition.