Several destinations within 2-3 hours of Chennai are worth a day trip.
Mahabalipuram (60 km south via the scenic East Coast Road along the Bay of Bengal) has Pallava rock-cut temples and shore temples from the 7th-8th centuries — some of the finest early Dravidian architecture in India. Easy by bus or taxi in a day.
Kanchipuram (75 km southwest) is the ancient Pallava capital with over 100 temples and the silk weaving workshops that produce the famous Kanchipuram saris. Also easy in a day.
Pondicherry (160 km south) warrants an overnight but can technically be done as a very long day trip. The French Quarter, Sri Aurobindo Ashram, and Auroville are the draws.
Crocodile Bank (50 km south on the East Coast Road) is India's largest crocodilian conservation centre — worth a stop on the way to Mahabalipuram, especially with children.