At IIT Madras, you’ll be provided with a hostel room at the time of admissions. But if you want to live outside the campus, you must check out some PGs or Rooms nearby.
Living outside the campus could be expensive. These are the places where you can look for accommodation- Adyar, Velachery, Besant Nagar, Thiruvanmiyur, and Mylapore.
Hope you find a good PG/Room for your stay.