The dry season (May to September) is the best time to visit. Skies are clear, the sea is calm, and visibility underwater is at its best — often 20–30 metres. July and August are peak season and the islands, particularly Trawangan, get crowded.
The wet season (November to March) brings rain and rougher seas. Crossings from Bangsal and Bali can be cancelled during bad weather, and visibility underwater drops significantly. Meno in particular, with the calmest water normally, suffers more during swells. That said, accommodation prices drop sharply and you'll have more of the islands to yourself.
April and October are transitional months — good weather overall, manageable crowds, and reasonable prices. June is often excellent: the crowds haven't peaked yet and conditions are ideal. Manta rays are occasionally seen off the southern tip of Trawangan between June and October, when seasonal upwellings bring colder, nutrient-rich water to the surface.