Short answer
When should most travellers go?
Papua New Guinea Tourism Promotion Authority identifies the dry season from May to October as the general best time for travel. Its more detailed planning guidance highlights June to September as the coolest and driest core period for many visitors.
These months are especially useful for trekking, Highland travel, birdwatching and major cultural festivals. They also reduce—without eliminating—the chance that heavy rain will affect roads, village access and smaller domestic flights.