After debating nearly seven years about where to move, the board of the Collegiate School, New York City’s oldest and one of its most prestigious private schools, announced Tuesday that it had purchased land for a new building between West 61st and 62nd Streets and between West End Avenue and Riverside Boulevard. It will be the 17th move for the school since its founding in New Amsterdam in 1628, but the first since 1892, when the West End Collegiate Church and the Collegiate School moved to the Upper West Side.