Kodaikanal is at 2,133 metres, which means it stays cool and pleasant when the plains below are roasting. The best months are October to March, when the skies are clearer and the air crisp at night. Days are mild at around 15–20°C; nights can drop to 8°C in January, so bring a layer.
April and May are peak season — the plains swelter and half of Madurai seems to drive up the hairpin road. Accommodation prices rise sharply, the lake is crowded, and traffic on the main road can be bad. If you have a choice, avoid these months.
The monsoon arrives in two waves: the southwest monsoon brings rain from June to August, and the northeast monsoon follows in October and November. The falls run well after rain, the forest turns vivid green, and the mist is near-constant. Travel to Kodaikanal in the monsoon if you like atmosphere and don't mind wet feet.