Delhi

Vivekanand institute of professional studies (VIPS). .

My take on the leading/popular institutes:
Vajiram
Sriram
Unique
ALS
Rau's
Key points to remember:
Make a checklist of what you expect from the institute
Ask questions like-
How are the providing the guidance?
Whats the course structure?
Who are the teachers?
What is the support they provide?
My views of the leading institutes:
Legacy: Vajiram
Mediocrity: Chanakya
Mini-Vajiram: Sriram
Heritage: Rau's
Better than Vajiram: ALS
Holistic learning: unique Shiksha

There is no proper cut-off. You will have to give entrance exam for MA in political science and on the basis of your entrance exam performance they will allot you a college and eligibility for giving entrance exam is securing 55% and above in B.A Honours in Political Science from any college affiliated to the University of Delhi or B.A (Hons.) in any one of the subject securing 60% aggregate.
Hope this helps.

Go through the college predictor below for details:
https://www.shiksha.com/b-tech/resources/ggsipu-college-predictor

GGSIPU 2018 College Predictor
Use your GGSIPU 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of GGSIPU 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/ggsipu-college-predictor.

GGSIPU 2018 College Predictor
Use your GGSIPU 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of GGSIPU 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/ggsipu-college-predictor.

Log in to DU portal for UG admission and login to the tab with your own particular Id. Then, a page is generated on the site with options for fee payment, college, cut-off released by DU. If you have any query regarding the same, comment in the box below.

You can go to South if you get top NITS. NITS in South are far more better than NSIT, Delhi. I am also studying in South from North. So I know there will be some problem at starting but South Indians are very good in nature. They will help you whenever you need them. Also, there is a good environment. So don't hesitate to go to South India.