Hi! In order to pursue your doctoral studies, you need to have a focused topic: the general area and the specific topic in that area. FT will require 3-4 years and PT will take about 5-8 years depending on how much time and effort you put.
Reg the unis, there are several... you will have to decide, based on your area of interest, availibility of good supervisors, proximity to your place of residence, FT or PT, etc.
To start with, there are the IIMs, IITs, and the IISc, besides certain NITs. Then, there are other regional universities that are pretty good, having their own standing... Remember that selection of the university is subjective and is your personal decision based on the above parameters.
All the best in your doctoral endeavours.
Vijay