The best time to visit is November to March, when temperatures are in the mid-20s and the monsoon has cleared. December and January see the most pleasant weather, though December also brings the most domestic tourists over the holiday period.
Avoid October through early November: the northeast monsoon hits this coast directly, bringing heavy rain and rough seas. July and August are hot and humid but workable. The Mahabalipuram Dance Festival, held in the open air against the backdrop of the monuments, takes place in January and is worth timing a visit around.
Chennai day-trippers arrive in large numbers on weekends. The sites are quietest early on weekday mornings.