If you are a General category student then I would say that you might get a seat in NITs in the 7th round or special round (if it is there this year) but that would definitely not among the top NITs or maybe IIIT i.e. you will be just following the brand name of NIT. Not to give you any false hopes the above might not happen and other than this you should go for the top private Institutes rather than the not so good NITs as their ROI - Return on Investment is better along with their brand names.

To check for colleges you can try career360, you can google for the top institutes in your region or else you can contact a guidance counsellor