NIT

NIT Tiruchirappalli, Tamil Nadu
http://nith.ac.in/
NIT Surathkal, Karnataka
http://www.nitk.ac.in/
NIT Rourkela, Orissa
http://www.nitrkl.ac.in/
MNIT Jaipur, Rajasthan
http://www.mnit.ac.in/
VNIT Nagpur, Maharashtra
http://www.vnit.ac.in/
SVNIT Surat, Gujarat
http://www.nitp.ac.in/php/home.php
NIT Allahabad, UP
http://www.nitap.in/
NIT Warangal, Telangana
http://www.nitw.ac.in/main/
NIT Durgapur, West Bengal
http://nitnagaland.ac.in/homenew/
NIT Agartala, Tripura
http://www.nitk.ac.in/
NIT2 Jalandhar, Punjab
http://www.nitj.ac.in/
MANIT Bhopal, Madhya Pradesh
http://www.web.manit.ac.in/
NIT Hamirpur, UP
http://nith.ac.in/
NIT Meghalaya
http://nitmeghalaya.in/nitm_web/index.php
NIT Kurukshetra, Haryana
http://www.nitkkr.ac.in/
NIT Silchar, Assam
http://www.nitk.ac.in/
NIT Srinagar J&K
http://www.web.manit.ac.in/
NIT Ponda, Goa
http://www.nitgoa.ac.in/
NIT Jamshedpur, Jharkhand
http://www.nitjsr.ac.in/
NIT Patna, Bihar
http://www.nitp.ac.in/php/home.php
NIT Delhihttp://nitdelhi.ac.in/
NIT Yupia, Andhra Pradesh
http://www.nitap.in/
NIT Puducherry
http://www.nitpy.ac.in/
NIT Sikkimhttp://www.nitk.ac.in/
NIT Dimapur, Nagaland
http://nitnagaland.ac.in/homenew/
NIT Imphal, Manipur
http://www.nitk.ac.in/
NIT Srinagar, Uttarakhand
http://www.web.manit.ac.in/
NIT Aizawl, Mizoram

The answer to this question includes political as well as logical touch although both the institutions are centrally funded. There is a large gap between the quality of students getting seats in an IIT as compared to the one getting a seat in NIT. Also, the government has to maintain a good image for the technical education system of India so the preference is given to the IITs. Although the amount of money does not very much which is around 3500 crores a year. The money issued for officials working in the institution, the fests held and the job perspective is more for IITs again for creating a good image worldwide. Also, the government is not that much capable of getting the NITs and IITs to the same level. The reason is that one needs to understand keeping in mind the political statistics. NITs are doing too good when it comes to education for a better future scope.

This is a dilemma many students face while selecting a college.
So let's take a look at the available options.
To be honest, I would say go for top private universities over lower-ranking NITs. But how low the rank can be.
I would suggest NITs as around 5th or 6th rank can be considered safe over the private universities.
But below this rank give preference to private universities.
Consider one more practical options. I would suggest after top 5 NITs, go for top government colleges in your state. This college would generally be better than private universities.
For example, in Maharashtra, you can go for College of Engineering, Pune or VJTI over private universities like VIT, SASTRA.
On a different note, I don't see BITS as some random private university, go for BITS-Pilani if you are not getting top 3 NITs (you can take BITS even if you are getting top NITs just saying).
So, consider your options properly before making a decision.

I think no engineering college guarantees placement to its students.In fact, engineering colleges are there to make you an engineering. Even the students of IIT endup jobless.
The condition of NITs (except the top NITs) is worst. Many newly established NITs are still struggling for campus and well as faculty members.
I am not saying that you should expect nothing. It is up to you and your calibre to get a good job offer.The placement cell can only invite the companies for you. Getting a job or not depends on you. If you have talent then you will surely get a good job offer even through off-campus placements. I have seen students of BIT Patna who failed to get a job through campus placement but got the job of around 30 LPA off campus.
You can expect a placement package as high as 1 crore and as low as zero. Now, I think that things are clear in your mind. NIT will only give you tag and knowledge. You can get jobs in PSUs as well. However, you can expect an average package.
Hope it helped.
Thanks.

There are some good institutes apart from IITs, NITs and IIITs. You can check this list:
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0. This list also includes IITs, NITs and IIITs. So, I will mention the colleges other than IITs, NITs and IIITs here:
BITS-Pilani
Indian Institute of Space Science and Technology
Anna University
IIST
DTU-Delhi
NSIT-Delhi
Jadavpur University
BIT Mesra, Ranchi
PSG College of Technology
Institute of Chemical Technology, Mumbai
PEC University of Technology
IIEST, Shibpur
TIET, Patiala
HBTU, Kanpur
College of Engineering, Pune
I am doubtful about these but some rank them higher so I will let you know (I personally believe that you should avoid these colleges)
VIT-Vellore
SRM
Apart from them some good colleges which you can go through JEE or KVPY are:
IISC
IISER
Also, check Indian Institute of Statistical Institute if you are passionate about maths.
All the best.

Following are the eligibility criteria to get admission in NIT
1. As per the revised criteria by MHRD you should have at least secured 75% marks in class 12th exam or be in the top 20 percentile in class 12th exam conducted by the respective boards and for a ST/SC category candidate eligibility criteria is 65% marks in class 12th.
2. You have to appear for JEE exam for which the criteria is depending on-a. Date of Birth of the candidate applying: Born on or after October 1, 1993(your category).b. Qualifying Examination: You should have passed 12th class or qualifying exam in 2016 or 2017 also student qualifying exam in 2018 can apply.c. Number of attempts in the Qualifying Examination: JEE Main aspirant can avail only 3 attempts for the national level undergraduate engineering entrance exam.
3. For BE/B.Tech you should have cleared 12th class examination with Mathematics and Physics as compulsory subjects along with one of the Chemistry/Language /Biology/ Technical Vocational subject whileis you are going for B.Arch/Planning you should have cleared 12th class examination with Mathematics.
The 31 NITs offer admission to about 18,000 students each year at present.