You are looking at what remains of the original Panama City. One of the cons of being a geographically desirable isthmus with the Atlantic on one side and the Caribbean on the other is the threat of plundering pirates.
Founded in the 1500s by the conquistador Pedro Arias de Avila the city was sacked in the 1670s by Welsh pirate Henry Morgan. The city consisted mainly of wood structures and was burned to the ground. The tower you see pictured is the remains of a cathedral. After the destruction the city was moved a few miles away to what is now Casco Viejo, which I will post on in the coming weeks.
Panama La Vieja, also known as Panama Viejo, is open every day except Monday from 8:30-6:30 p.m. Admission to the site is $4 and $2 more to enter the museum.