Three new private schools in Manhattan will open in September, despite rumors that cash-strapped families are pulling children out of expensive private schools. Consultants say starting a new school in New York is difficult, even during good economic conditions, because the real estate and insurance costs are high. Six months ago, former Esquire magazine owner Christopher White canceled plans to open a private school called Nations Academy because financing fell through and developer Durst Organization pulled out of the project. The new schools — Greenwich Village High School at 30 Vandam Street, Claremont Preparatory High School at 41 Broad Street and Aaron Academy at 309 East 45th Street — have tuitions ranging from $31,500 to $45,500 per year, and said despite the recession, parents are interested in the schools.