Founded in 1936, Kalakshetra is a leading serious school of Tamil classical dance and music (sponsoring many students from disadvantaged backgrounds), set in beautiful, shady grounds in south Chennai. During morning class times visitors can (quietly) wander the complex. Across the road is the Kalakshetra Craft Centre (Indian/foreigner ₹100/500), where you can see Kanchipuram-style hand-loom weaving, textile block-printing and the fascinating, rare art of kalamkari (hand-painting on textiles with vegetable dyes); if you're feeling inspired, there are courses, too. For upcoming performances, check the website.
The Thiruvanmiyur bus stand, terminus of many city bus routes, is 500m southwest of the Kalakshetra entrance.