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.