I am from Jharkhand and want to pursue BCA. Is it worth going to Chennai or Bangalore for BCA or should I try in Kolkata or Delhi?

Being a Graduate degree you can pursue, it in Chennai itself as many North Indian students are studying here and cost of Living is also cheaper to other states.

It would depend on the college you choose. Almost all the above cities have really good college. I suggest you look for a good college rather than just the city. Only good colleges can offer you great placement opportunities.