If looking for an institution not excessively focused on the academic grind Indian ishtyle, you might add the Krishnamurti School to your list of options to investigate. Its new location is just off the OMR, ~20 km from Adyar, in Thalambur. I know nothing about the school itself, but I've heard that the kids in the non-IIT/IIM track are allowed to look out of the window every once in a while.