Here are some of the colleges given below you can prfer for M.tech programme-

Indian Institute of Technology Madras

National Institute of Technology Tiruchirappalli

PSG College of Technology, Coimbatore

Amrita School of Engineering, Coimbatore

You can check the further colleges with the given below link.

https://engineering.careers360.com/colleges/list-of-me-mtech-colleges-in-tamil-nadu

Good Luck!