To repeat myself: I don’t think that the choices are limited to university/college music schools or free standing conservatories (the latter tend to be expensive, as a generalization). Again, he is young. He may end up wanting a BA or BS in music or something else and continue to play.
The focus on enjoyment, suggested by everyone, suggests that music be enjoyed for the present, not for the sake of admissions, while you, the parent, know full well that certain things need to be done. As I wrote before, it is a difficult balance.