Hello dear. 

ar student,

List of few Colleges under NATA is here:

Sir JJ College of Architecture, Mumbai

Dy Patil college Architecture, Pune

CEPT University, Ahmedabad

Sushant School of Art and Architecture, Gurgaon

Sinhgad College of Architecture, Pune

School of Architecture, R.V. College of Engineering, Bangalore

SRM University, Multiple Locations

Jamia Milia Islamia, New Delhi

Manipal University, Faculty of Architecture, Multiple Locations

IP University, New Delhi

Hope it helps.

Best of luck..

As you are asking ,I  tell you one thing government college is always better than private due to the money means fees and other charges. IET Lucknow,KNIT Sultanpur and BIET Jhansi are the best developed in all means .and other colleges as you mentioned is also good to talk admission.in my opinion your sequence is absolutely right.