The dry season (April to October) is the best time to visit Bromo. Clear mornings are most common between May and September; the sunrise viewpoint is only worthwhile if the sky is clear, and July and August are the most reliable months. The caldera is a very exposed environment: even in the dry season, cloud and mist descend at any time.
The wet season (November to March) brings cloud and rain that frequently obscures the caldera. January and February are the wettest months, and the dirt tracks in the caldera can become impassable after heavy rain. The Kasada festival falls in the dry season, usually July or August; attending it is a reason to plan specifically around dates.
Morning visits are essential for the crater experience. The Park entrance opens at around 4am; most jeep tours from Cemoro Lawang depart between 3 and 4am. By 9am, tour groups have largely dispersed and the park becomes quieter, though you lose the sunrise light.