See, you have scored a very good rank and with a CRL of 3866, you can get every National Institute of Technology that you might want. If you want to get the top 3 NITs, you won't be getting Computer Science and Engineering there, however, you may easily get Electrical, ECE etc. If you start from NIT Allahabad, you can easily get CSE or IT depending on your state and this year's counselling. The best NITs you may get are:

NIT Trichy
NIT Warangal
NIT Rourkela
NIT Allahabad

You can also use our college predictor to see your chances in all the colleges:
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Hope I have answered your question. All the best!