Battery Tower was the name of a proposed initial unit of a $50,000,000 1929 residential development on West Street in the Financial District of Manhattan, New York City, near Battery Park. It would have been the first hotel-apartment completed in the Financial District. It became one of a number of skyscraper projects left unfinished. Battery Park City was …Battery Tower was the name of a proposed initial unit of a $50,000,000 1929 residential development on West Street in the Financial District of Manhattan, New York City, near Battery Park. It would have been the first hotel-apartment completed in the Financial District. It became one of a number of skyscraper projects left unfinished. Battery Park City was built on the site of the proposed development, nearly six decades later.