I get this question all the time.  Here’s a list of the all-boys independent schools, ranked, in alphabetical order:

Allen-Stevenson School

Browning School

Buckley School

Collegiate School

Saint David’s School

St. Bernard’s School

For a directory, look at: NYC Private Boys Schools Contact Info  Note that Saint David’s is a Catholic independent school.

Only Collegiate and Browning go all the way from kindergarten to 12th grade.