To do master’s in any engineering domain pefer government institute affiliated colleges or government institute. But you are the person going to study. So before choosing an institute analyse all the factors like placement,education, entertainment, etc.
In means of Tamil nadu. PSG institute of technology is best college to study automobile related courses and Madras institute of technology also offers automotive engineering in M. Tec. And another things is if u decided to do higher studies go in more specific sectors like engineering design and internal combustion engine like courses.