NIT

I know, you've gone through a lot. Now calm, relax and enjoy every moment of your life. Now, you will be able to do all the things you couldn't during your Prep. Binge Watch Web series, Play video games, Visit your Nani, Bua, Taya, Tais house, meet your old friends, play with your cousins. Huh, just relax now. You're going to be on a crazy ride of 4 years in which you'll go through first experiences of many things, road trips, memories, heartbreaks and what not!
My Answer may be too long but I strongly recommend you to read it. Let me make selecting a college easier for you. First of all, be happy, you have manage to get a decent score. Don't Let that Decent word disappoint you, remind yourself that you're still better than the 96% of the people out there. PAT yourself on the back for landing amongst the top 4 percentile of the so called the toughest exams of the world. I had the same rank during my time. There are many good choices available for you at this rank, though you have to accept that you won't be able to get a good branch in top 45 NITs (I know, in most cases you'll probably have to miss out on the Brand- Tag of NITs, IIITs, But reality is completely different, NITs in these days aren't a good choice but a trap for clueless and Brand Conscious people, If you don't fall into this trap, You will surely end up doing better than most of the NITians, But for that you need to select the perfect college for you, so let's begin!)
Choose A Branch (This Is Really Important, Very Important!)
You have to make sure that you're choosing this out of interest, else there's no point of the hard work, you did to crack JEE, and reach till here. Let me simplify this for you a bit, if you had a Computer Science Subject in your 1112th and were scoring well in it, go for CSE. If you were good at Current Electricity, AC and Semiconductors go for ECE or EEE. If you were good at Mechanics, go for Mechanical Branch. Selecting a Branch is as simple as that, but people usually tend to get distracted by the opinions of the sheeps and end up going numb and clueless. See, it is really simple - Select a branch your good at fundamentals of which. TIP: don't go for a branch that you don't know the fundamentals of/ weren't good at, just because it has higher placements/cutoffs.
2. Look for the colleges which offer good facilities for your selected branch
I also did my bit of research for My Branch (CSE)