Amravati has a lot of light pollution, so can't shoot milky way over there. Maybe in the neighbouring villages, but anyways it's raining all over there.
There's a place called Nagalapuram, 3 hours from Chennai. It is said to have the most starry night in South India. On a cloudless winter night, you can easily spot Orion Nebula and Beehive cluster. Kodaikanal can be your second choice.