There are several institutions that can lay claim to that title and there would be no name or list of the best which cannot be contested, and spark debate or controversy. Many ranking and awards that have come up lately (and more get added to the list each year) which publish raking across multiple categories (and categories also increase every year to accommodate more and more schools) which offer some insights, however there no neutral independent entity with no commercial relations with schools that exists to definitely pass best and worst school judgement with any objectivity.
While we all agree that some schools do a better job than others, in India, which has 1500+ boarding schools, finding the best one could across all parameters would not only be very difficult it may be impossible. So each set of parents have to find the best one which suits their needs and aspirations. Some things that a parent must keep in mind:
Don’t go overboard, there is little correlation between expense and output desired.
ii) Academic output:
Ask for past three years results if you want an academic rigorous environment.
iii) Look at infra in detail and objectively:
There are certain sports and activities which appear attractive on paper but have very little value practically.