My brother is currently studying IT at IIIT Allahabad and according to his first-hand experience and your interest in IT, the order of preference for you should be:
IIITA>MNNIT>BITM>MANIT
It is because if you are genuinely interested in IT then IIIT Allahabad is the best option you can choose because of the following key points:
In NITs, you need to study a lot of subjects not at all related to your branch or course!
However, MNNIT or BIT Mesra may prove to be better options in case you realize that computers are not your cup of tea and decide to go into the non-tech sector. You will have a lot of diverse companies visiting these campuses, while in IIIT Allahabad you’ll see only IT companies coming to recruit.
Also, JEE Main rank of all the options you mentioned will differ from each other. So your rank also plays a major role in selection.