Which would be the best option, CSE in RVCE vs EEE in NIT Surathkal/Rourkela/Calicut or ECE in BITS Goa? I am not very keen in computer science but I am looking for good placements.

You should definitely go for NITs. NITs will offer a better crowd, alongside good alumni networks. NITs also often come with a better campus and comparably lesser fees. The major upside of choosing NIT is it comes with a cooperative faculty and provides placement in various core companies, making both EEE and ECE courses quite good as a choice.

Moreover, every NITs offer multiple opportunities and has better fests. On the other hand, BITS Goa is reasonably expensive. 

If you are interested in CSE, then opting for RVCE can be better. And your second choice about opting for EEE or ECE at NIT Surathkal or Rourkela can be a decent decision as well. 

You should choose the institute that is close to your residence and finalize your decision after considering every relevant factor alike.