Kapaleeshwarar Temple in Mylapore is certainly one of the oldest and most important Shiva temples in Chennai and is well worth visiting.
If you are particularly interested in Amman temples, you could also visit the Kalikambal Temple in George Town, which is an old and well-known temple in Chennai.
Ashtalakshmi Temple at Besant Nagar is also worth visiting, although it is a comparatively modern temple and not an ancient one.
If your main interest is specifically in very old temples within Chennai city, I would definitely start with Mylapore.