IDEA, or the International Dialects of English Archive, collects recordings of people talking in English.
The "India" section has recordings of English speakers from Lucknow (who, we are told, "exemplifies the lack of aspiration on initial [p], [t] and [k]"), Hyderabad, Chennai, Trivandrum, Gujarat and someone from "Northern India".
You know what would be really cool? Sound recordings of all Indian languages and dialects. There are Indian languages such as "Yakha" and "Kok Borok" and "Pankhu" and I have *no* idea how they sound.