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...)
in Chennai you can go to mahabalipuram,vedanthangal (bird watching), Golden Beach, Theospophical society in Adyar, marina beach, ECR road (famous outing)
Chennai is a nice place.It is a well connected city and good in telecommunications as well.You would also get Spicy food from places like Saravana Bhavan and Vasantha Bhavan and also you can get to see places like Spencers and City Centre.Besides we have own own second longest beach in the world and adding to it were temples.
The best time to visit Chennai is end of December to first week of January.It is a city of temples.Best place is Marina Sea Beach.