Check out Cholamandalam Artists's village on ECR. They have some real good stuff but may be on the higher end.

There are some art galleris like Vipaksha, Apparao etc. - I have only read about them though.

Poompuhar - the TN's government's handicraft showrooms are in many places in TN. They are a decent bet.

Victoria Technical Insitute on Mount Road in Chennai is said to have really good stuff. But it's slightly pricey compared to other places.