Once upon a time the Catholic Church built a school for boys, particularly geared towards entering the priesthood. It stood on top of Grymes Hill near the site of Wagner College (initially a Lutheran seminary. I wonder if they raided each others' campus.) looking over Clove Valley. In 1969 it closed due to declining enrollment. It became a retreat house (and I seem to recall my friend's father going there on retreat) and was eventually sold to developers in 1985. After that it fell into a sad state of ruin before finally being demolished over the past few years.
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I'm not the only one interested in Staten Island's fallen buildings. Here's a nice site with pictures of the Academy's sorry state prior to its destruction.