I think it depends on when you are going to travel and cities you want to visit within India. If you are coming for a long holiday and plan to visit whole of India, then the best time to visit is September to November and Feb to Mid of March. The weather is pleasant during this time.
But if you arrive in summers, you can go to one of many hill stations with pleasant weather. Travelling between mid May to July is not recommended as its Monsoon time and most cities get affected by heavy rainfall during this time.
