Would you be a day student at either place? Much easier to go to NEC from Andover or Juilliard from Choate if a parent is driving you.
Or, if you went to Andover, would you study cello with the teacher there, or would you study with somebody at NEC? Same question for Choate. I ask because if you are a very advanced cellist, the teacher matters a lot. My own child also was accepted to both of these schools but chose another, partially because of this issue!