Hi Suraj, You can head to Tadiandamol hill in the district of Coorg in Karnataka as it is good star gazing spot. You can also choose to go to Yercaud in Tamil Nadu, Neil Island in Andaman and Nicobar, Shahapur in Maharashtra or Lonar Crater in Maharashtra. Find more about capturing Milky way in attached article below. Keep exploring!
I doubt, there is any perfect place in South India for witnessing the Milky Way. Having said that, i have partially seen it at Sharavathi Valley in early November and it was beautiful. Though it was not as clear as what one can see @Spiti and @Sarchu. Good Luck :)