Western Java has a long wet season from October to April, with the heaviest rains in December and January. The slopes of Mount Karang and Pulosari catch a lot of it; trails are slippery and the leeches come out in force. Ujung Kulon is more or less inaccessible during the peak of the rains because of rough seas in the strait.
The dry season from May to September is the obvious window — sunny days, manageable humidity, calm strait crossings to Anak Krakatau and Ujung Kulon. Avoid Idul Fitri week if you can, when Jakarta empties into Carita and Anyer and the coastal road becomes impassable.