Hello here is the list of all NITs

1.) National Institute of Technology, Tiruchirappali

2.) National Institute of Technology,  Surathkal

3.) National Institute of Technology,  Warangal

4.) National Institute of Technology, Calicut

Thank you and all the best to you

Yes almost all NITs offer ECE and Mechanical engineering courses.

Some of the NITs in South India are:

1. NIT TRICHY
2. NIT SURATHKAL
3. NIT WARANGAL
4. NIT CALICUT

I hope this helps you!