 The Lord Mayor 's official residence is 3 Elliot Terrace , located on the Hoe . Once a home of Waldorf and Nancy Astor , it was given by Lady Astor to the City of Plymouth as an official residence for future Lord Mayors and is also used today for civic hospitality , as lodgings for visiting dignitaries and High Court judges and it is also available to hire for private events . The Civic Centre municipal office building in Armada Way became a listed building in June 2007 because of its quality and period features , but has become the centre of a controversy as the council planned for its demolition estimating that it could cost £ 40m to refurbish it , resulting in possible job losses . 
