Hey S.M ,
Greetings!

As per your query - list of best colleges offering Automobile Engineering other than IITs and NITs are:-

BITS Pilani

Lovely Professional University, Punjab

Delhi College of Engineering

PSG Technology Coimbatore

National Institute of Engineering, Mysore

BIT Ranchi

NSIT, New Delhi

College of Engineering, Pune

Jamia Millia Islamia, Delhi

Good Luck ! You can reply to this comment if you have any further queries , I will be happy to help .