Engineering colleges in Mysore:

1. The national institute of technology, Mysore
2. Shri jayachamarajendra college of engineering
3. Vidyavardhaka college of engineering
4. JSS science and technology university
5. Maharaja institute of technology

You can check more engineering colleges in Mysore here,

https://engineering.careers360.com/colleges/ranking/top-engineering-colleges-in-mysuru

Engineering colleges in Bangalore:

1. BMS college of engineering
2. RV college of engineering
3. PES university, Bangalore
4. New Horizon college of engineering
5. CMR institute of technology

You can check more engineering colleges in Bangalore here,

https://engineering.careers360.com/colleges/ranking/top-engineering-colleges-in-bangalore

Hope this will help.