What I remember most about Chennai is the roti and veg curry. Its a must try just be careful of the spice if you dont like it to hot.
in Chennai you can go to mahabalipuram,vedanthangal (bird watching), Golden Beach, Theospophical society in Adyar, marina beach, ECR road (famous outing)
The two most interesting places are Marina Beach : a lot of women wearing saree take a bath there, it's wonderful to take beautiful pictures. And Kapaleeshwara temple. I was lucky when I went there on evening cause there was an engagement ceremony... I haven't visited the museum because the price was around 10 or 20 times higher than for local people (I can understand when it's higher but not so much...)
It is very hot but people are nice and food are tasty with the exception of drinking water which is salty.