Philip Academy, Andover, MA and Philip Exeter Academy, Exeter, NH
Both are super hot best 'elite' high schools. extremely competitive. if the kid from 'low-income' family get in, most of them can have scholarships.

St Paul School at Concord NH is also another top 'elite' private school.

Both of Philip as well offer the Summer program. There are quite a few kids enrolled from Taiwan, South Korea, Japan and HK.

Good luck