How do centres like CCG, and CIIPC compare to centres like Vidhi, ORF etc? Which are the good places to intern?

Quite different in terms of the work that they do. You can't compare career policy bodies with research centres affiliated to a university. Both the centres are doing good work, though CIIPC is less than what it used to be under Arul.

Which one is better for an internship in terms of CV value between Vidhi and CIIPC?

Vidhi of course.

NLUD centres are pretty good especially CIIPC, CCG, and P39A. They are probably on the same pedestal as Vidhi etc.

No, they are good enough among the NLU research centres, but nowhere close to the CV value of Vidhi. Don't get carried away.

P39A is way ahead w.r.t prestige and cv value.