Tamil Nadu

Some of the best engineering colleges in Tamil Nadu or Chennai which offer lateral entry admission after Diploma in ME are mentioned below:
1) Chennai Institute of Technology, Kundrathur
2) Hindustan Institute of Technology and Science, Chennai
3) R. M. K. Engineering College, Tamil Nadu
4) Kalasalingam Academy of Research and Higher Education, Virudhunagar
5) PDM College of Engineering, Bahadurgarh
Regards.

This is the link to the admission portal for the course:
http://www.vit.ac.in/files/UG/index.html

I think ASB Coimbatore is a better option amongst the two. There are many good colleges if you consider relocating yourself, especially around Mumbai region for finance.

There are over 11 Flying / Pilot Training colleges in Tamil Nadu. Please refer to the link provided below for a list of these colleges. You can navigate to a school of your choice using the filters on the web page. All the schools mentioned at the link below have good placement. https://www.shiksha.com/aviation/flying-pilot-training/colleges/colleges-tamil-nadu.

Please refer to the link provided below for a list of all institutes which offer pilot training courses in Chennai. There are over 8 such institutes, and you can navigate to a college of your choice using the filters on the web page. https://www.shiksha.com/aviation/flying-pilot-training/colleges/colleges-chennai.