Indian Institute of Technology, Mumbai: Not only is the Powai campus beautiful, it offers great options for PhD in Humanities, Science, Technology and Social Sciences.
University of Mumbai: It has so many different departments including for humanities and sciences that you'll never be short on options.
Dr DY Patil University, Navi Mumbai: This university has a few different courses and PhD options like PhD in Education. And it's pretty good for sciences and technology courses.
Amity University, Mumbai: Do you feel like pursuing PhD in Aerospace, this is the place for you! A university great for campus life and academics, it has a lot of good options for PhD.
Tata Institute of Social Sciences: As the name suggests, it's for social sciences mainly. You will get access to some of the best faculty around. Research is their core speicality and it's highly competitive.