First of all, none of the NITs have an aerospace engineering department. But you can do your graduation in mechanical engineering and get into the aerospace industry. Even students from civil, chemical, electrical and electronics can become aerospace engineers.
Now assuming that you want to do your bachelors degree in aerospace engineeing and you really want to learn the subjects properly, then the following institutes are the best options available:

1. IITs(B,K,Kgp and M)
2. IIST, thiruvananthapuram
3. Madras Institute of technology
4. BIT mesra

following are the IITs that offer BTech in aerospace engineering 

IIT Kanpur

IIT Madras

IIT Kharagpur

IIT Bombay

IIEST Shibpur

all you need is 60% marks in class 12 aggregate subjects and you need to score above 200 to have a solid chance in the above-mentioned IITs regarding IISET 180-200 is enough

 all the best!!!