Four days in Panama City: the world's shipping queues up at the end of the street

Casco Viejo is the second Panama City, built in 1673 on a peninsula that could be walled off, after Henry Morgan made the first one untenable. It stayed the whole city for two hundred years, then the money moved east and left it to decay, and it has spent the last two decades being pulled back. The result is a grid of plazas, church towers and balconied townhouses in which about a third of the buildings are immaculate, a third are scaffolded and a third are still roofless.

Walk it rather than tick it off. Plaza de la Independencia has the cathedral with its two mother-of-pearl towers, Plaza Bolívar is the quiet one, and the church of San José holds the golden altar that legend says was whitewashed to hide it from Morgan. On the seaward side, the Paseo Esteban Huertas runs along the top of the old sea wall under bougainvillea, with Guna women selling molas, the layered appliqué panels from the San Blas islands, spread out on the stone.

Then give an hour to the canal museum on the main square, which is much better than its size suggests: the French attempt of the 1880s that killed twenty-odd thousand men and went bankrupt, the American takeover, the engineering, and the long negotiation that ended with Panama taking the canal over at noon on the last day of 1999. Eat on a rooftop afterwards, because the skyline across the water at night is the other half of this city's argument with itself.

Go to Miraflores early. The locks are twenty minutes from the centre, the visitor centre has a viewing platform right over the chamber, and the traffic is heaviest in the morning. What you are watching is straightforward and does not stop being extraordinary: a ship comes in with metres to spare on each side, the gates close, and water is let in by gravity alone until the ship has risen the height of a three-storey building. No pumps are involved anywhere in the canal. These are the original locks, in service since 1914.

The museum inside covers the construction, the yellow fever and malaria campaign that made it possible, and the 2016 expansion that added a second, wider set of locks alongside for the ships that no longer fit. Check the day's transit schedule before you go, because between the morning and afternoon convoys there can be a quiet hour with nothing in the chamber.

In the afternoon take the Amador Causeway, a three-kilometre road out into the bay linking four small islands, built from rock excavated from the Culebra Cut and later a US defensive position guarding the canal mouth. It is now where Panama City jogs, cycles and eats fish, with the ships waiting at anchor on one side and the skyline on the other. The Biomuseo stands at the landward end: a Frank Gehry building in colliding sheets of red, yellow and blue, on the theme of what happened when the isthmus rose from the sea and joined two continents together.

Panama Viejo is the first city, six kilometres east, and it has been left as ruins rather than rebuilt. The cathedral tower still stands to its full height with the roofless nave behind it, and around it are the footings of the convents, the bishop's house, the bridge and the slave market, laid out on mown grass beside the sea. The city stood here for a hundred and fifty years as the transfer point for Peruvian silver, which is precisely why Morgan wanted it.

There is a good modern museum at the entrance with a scale model that makes sense of the site, and a viewing platform in the tower. Take the advice from the staff about which edges of the park to stay away from: the ruins are surrounded by ordinary neighbourhoods and one side of it is not somewhere to wander.

In the afternoon, the Metropolitan Natural Park. It is a genuine patch of tropical forest with proper trails inside the city boundary, ten minutes from the towers, and it holds sloths, agoutis, coatis, toucans and well over two hundred bird species. Sign in at the gate, take the trail that climbs to the mirador, and you get the entire skyline framed by trees with the canal behind it. Go early or late in the day if you want to see anything with fur on it.

Cerro Ancón is the hill behind the old Canal Zone and the highest point in the city, and the walk up it is a paved road with almost no traffic on it, about fifteen minutes from the gate. It was inside American-administered territory until the handover, which is why there is forest on it rather than houses, and there are sloths and toucans in the trees on the way up. At the top, a very large Panamanian flag and a view that takes in Casco Viejo, the towers, the Bridge of the Americas and the canal entrance in one sweep.

Come down and finish in Casco Viejo at the San Felipe Neri market, a clean, cool, air-conditioned wet market a couple of blocks off the plazas, with the street stalls spilling around it outside. It is a good place to buy fruit you cannot identify and to sit down with a cold drink before a flight.

Then Tocumen, which is 25 km east and needs more time than the distance suggests. The Corredor Sur toll road is quick when it is quick and stationary when it is not, so leave three hours before an international departure.