NYC’s priciest private schools are spending millions to win an amenity arms race

Rooftop vegetable farms, playgrounds conceived by famous toy designers, and installations by blue-chip artists are among the top selling points at these private campuses.

At Marymount School, a private all-girls high school on the Upper East Side of Manhattan, students can pick fresh basil and chard from the rooftop farm, take a quiet moment of reflection in a minimalist chapel, or catch up on homework in one of the school’s many lounges. Their recently completed 10-story building, by the architecture firm Cookfox...