Set on the ground level of Spanish Navy headquarters, this museum has a great story to tell. It covers the greatest hits of Spanish naval pre-eminence, including the discovery and exploration of the Americas, the Spanish Armada, and the feared Spanish galleons of the 17th and 18th centuries. Juan de la Cosa’s beautiful hand-drawn map from 1500 is said to be the oldest map of Europe that shows the Americas. A scale model of Columbus’s flagship, the Santa Maria, shows what a fat little tub it was. By contrast, the cutaway model of an 18th-century galleon bristling with cannons can be seen as the birth of the modern warship. Coverage of the Battle of Trafalgar might make you forget that the Spanish lost. At the time of writing the museum was closed for refurbishment, although temporary exhibitions continue. Check the website for updates; when it does reopen, bear in mind you’ll need to show your passport to get in. The Navy runs a tight ship.