Students will also be heading to class right across the street at 26 Broadway in the iconic building that once housed the offices of John D. Rockefeller, where the Alliance for Downtown New York says the city's Department of Education has signed two 200,000-square-foot leases of its own.

"I'd say there's a proliferation of schools in Lower Manhattan," says Liz Berger, president of Downtown Alliance. She adds this is just the next generation of residential supporting commercial, pointing out ongoing construction of the Spruce Street school in the Ratner building and the Green School at site 2-B.

Of the Claremont School, Berger says "it's a for-profit school, a business that's decided that it makes good business sense to expand in Lower Manhattan."