Indonesia is too large and varied for a single trip to cover. Most first-time visitors do a version of the Java–Bali route. Repeat visitors tend to go further east.
The classic route runs from Jakarta to Yogyakarta (by night train, ideally), where you base yourself for Borobudur, Prambanan, and the city itself. Then east to Mount Bromo for the volcanic sunrise, and on to the ferry crossing into Bali. From Bali, the logical next step is Lombok and the Gili Islands.
For culture, Yogyakarta is the centre of Javanese court culture — wayang puppet theatre, batik workshops, kraton (palace), and the best base for the temple complexes. Tana Toraja in Sulawesi is more remote but extraordinary, particularly during funeral season (June–August).
For nature, the choices are enormous. Orangutans are most reliably seen in Sumatra's Bukit Lawang or Kalimantan's Tanjung Puting National Park, where the boat journey up the Sekonyer river into the forest is part of the experience. Komodo National Park is unmissable for the dragons and the diving. Raja Ampat, if you can afford the journey, is the finest underwater environment in the world.
For diving and snorkelling, Indonesia has more options than any other country. Bunaken (North Sulawesi), Komodo, the Banda Sea, the Gili Islands, Nusa Penida, Raja Ampat, Wakatobi — each offers something different. Wakatobi is the most isolated and perhaps the most pristine, while Bunaken has wall diving that drops 40 metres to a vertical garden of coral.
For surf, Bali is the most accessible with the most infrastructure, but the waves at Uluwatu, Padang Padang, and Keramas are excellent. Lombok's south coast, Sumbawa, Sumba, and the Mentawai Islands off Sumatra's west coast are for serious surfers who want distance from the crowds.
For the beaten track, Bali and the Yogyakarta–Bromo–Bali route remain genuinely worthwhile regardless of the crowds. The infrastructure is there for a reason.
For the road less travelled, look at Flores and the islands east of it — Sumba, Alor, Lembata — where tourism is still minimal and the cultures remain vivid.