Thanks for the inquiry. Since your son has a green card, your son has some more options. He can go to one of good/better public schools or to private day schools or boarding schools. while public schools requires your residence where the school is located for entering school, private school, especially elite private school requires what the top boarding schools requires, although admission criteria might be different depending on the mission and character of the schools.
If your son is aiming one of top universities in us, I recommend for him to apply one of top private schools which has higher success rate of sending their graduates to go the top universities in USA. In order to get accepted to this type of school, your son needs good preparation and strategies for admission.
If your son goes by himself to a high school, options are limited. Your son should apply to boarding schools or to private elite day schools with good student management program or guardianship program that focuses on helping students succeed at schools.
From preparing to apply to high schools to applying universities/colleges will take a longer, yet serious management program with professional guidance, especially for international students. We are more than happy to hear more about your son and love to discuss various options with you. Please contact us.