If you can afford BITS then just go for it. There is no point in studying in lesser known NITs. BITS have centralized placements. So almost all BITs students from different campus get good job offers. You will love it there because:
1. There is no reservation policy, so everybody there has almost the same level of intelligence and merit.
2. There is no regional feeling as there is no home state quota.
3. Good amount of exposures to industry through compulsory internships both in second and third years.
4. Innovative curriculum. BITS follow BE, unlike BTech followed in NITs. Unlike BTech, BE the first year syllabus is different for different branches.
5. They have a provision of 6 month thesis semester at an industry or lab, this enhances your skills exponentially and also paves way for a potential placement in the company where you do your thesis.