Indian Institute of Technology: Not only does one of India's premier institute for engineering have option for science stream, you can get PhD in Humanities and Social Sciences. Choose the city you want!
University of Delhi: It has so many different departments and schools, that whichever stream you pick up, you can pursue your PhD over here.
Jadavpur University, Kolkata: This university is great for Humanities and Social Sciences students, but it's PhDs in English are highly sought after.
Jawarharlal Nehru University, Delhi: JNU is one of the top universities to do your PhD in. It's competitive, but also one of the most economical PhDs in India.
Tata Institute of Social Sciences: As the name suggests, it's for social sciences. You will get access to some of the best faculty around.