The dry season runs from December to April and is the best time to visit: clearer skies, more reliable views from the volcano summits, easier hiking on the mud-prone Maderas trail, and warmer evenings. December and January are the most popular months and accommodation can fill up at New Year and during Semana Santa (the week before Easter), which is the busiest local holiday.
The wet season (May to November) brings afternoon thunderstorms but is otherwise still perfectly liveable — mornings are usually clear, the island turns lush and green, and waterfalls like San Ramón run at full force. October is the wettest month and the cloudiest; the volcano summits are often invisible for days at a stretch.
The Fiesta de San Diego in Altagracia, held in the second week of November, is the biggest cultural event on the island, with traditional dances and processions. The Fiesta de la Virgen del Carmen in Moyogalpa in mid-July is the other date worth timing a visit around if you are interested in local festivals.