Hey,
Here is the list of some of the best Engineering colleges in Mysore:
1. The National Institute of Technology,Mysore
2.NIE Institute of Technology,Mysore
3.Vidyavardhaka College of Engineering,Mysore
4.Academy for Technical and Management Excellence,Mysore
Hope this helps.
Good luck.

Below are the top colleges in Mysore for engineering

JSS Science and Technology University, Mysuru

The National Institute of Engineering, Mysore

Vidyavardhaka College of Engineering, Mysore

Good Luck!!