Derry City Council's Harbour Museum is situated at what is now called Harbour Square. Previously this was referred to as King's Quay. My recollection is that this area was cobbled until at least the late 1960's as were the lands on the riverside of the Guildhall where there was a carpark which was superintended by the Harbour Police, in particular Sgt. Lyttle.
This Italiante building was constructed for the Londonderry Port and Harbour Commissioners in 1882 by a Mr M McClelland to the designs of a John Kennedy. Both architect and builder were local. The original harbour office had been at Ship Quay but during the 1870's the Commissioners moved to the site now occupied by the Bank of Ireland at the junction of Strand Road and Sackville Street.
It is a two storey seven bay building with a square clock tower and aedicule doorway and dentilled cornice. Ownership passed to the Commissioners on 6th March 1885 consequent upon a tripartite deed between the Irish Society, (first part), Londonderry Corporation (second part,) and Londonderry Port and Harbour Commissioners, (3rd part.) The building is erected on the lands coloured green and blue on the terchart shown below. The Council purchased it from the Harbour Commissioners by deed dated 13th May 1991. The price paid was two hundred and thirty thousand pounds.
Sources: "City of Derry," An Hisorical Gazetter to the Buildings of Londonderry by Daniel Calley.
NIEA - Historic Building Database.