Eleven days from Lisbon to Seville: the bit in the middle nobody stops for

Land, get into town, and start at the bottom. Praca do Comercio is the square the rebuilt city was designed around, open on one side to the Tagus, with an arch at the far end that leads into the grid of the Baixa. It was the site of the royal palace until the earthquake and tsunami of 1755 took the palace, the square and about a third of the city with it.

Walk north through the grid and take the Santa Justa Lift up. It is a wrought iron tower from 1902, built to save people the climb from the lower town to the upper, and it looks so much like Eiffel's work that half the guidebooks credit him with it. The queue at street level is long enough that most people give up. Walk up the hill behind it instead and enter from the top, which is free.

At the top is the Carmo convent, whose roof came down in the earthquake and was never replaced. It has been left as a shell: gothic arches open to the sky, with a small archaeology museum in the apse. It is the best thing in central Lisbon and the only building that still shows you what happened here.

Then eat late and downhill.

Go up early. The Castelo de Sao Jorge sits on the highest of Lisbon's hills, has been fortified since the Moorish period and occupied since the eighth century BC, and what you buy with the ticket is less the castle than the platform: the entire lower city, the river, both bridges and the far bank. The first hour after opening is the one worth having.

Walk down through Alfama, which is the quarter the earthquake mostly spared, and it shows: no grid, no logic, lanes a metre wide, washing across the street, and cats. Stop at the Miradouro de Santa Luzia, a tiled terrace with bougainvillea over it and the whole of the quarter dropping away below.

At the bottom is the cathedral, begun in 1147 immediately after the city was taken from the Moors, built like a fortress because it partly was one, and repaired after every earthquake since. It is severe and dark and takes twenty minutes.

Keep the evening for fado. The genre was born in these streets and the tourist versions are everywhere, so go to a small room with a cover charge and no photographs allowed, and eat before you arrive.

Belem is five kilometres downriver and the reason to go is one building. The Jeronimos monastery was begun in 1501, paid for out of the tax on the spice trade that Vasco da Gama's voyage opened, and built in the Manueline style, which is late Gothic with ropes, coral, artichokes and navigational instruments carved into it. The church is free and the cloister is not; pay for the cloister. Da Gama is buried just inside the door.

Ten minutes' walk downriver is the Torre de Belem, a small fortified tower from the same decade standing in the water, part lighthouse and part customs post, with a rhinoceros head carved under one turret, copied from the animal the king was sent in 1515. Queues are worse than the monastery and the inside is small; the outside is most of it.

Then the coach museum, which sounds unpromising and is not. It holds more royal carriages than anywhere else on earth, and the eighteenth century Portuguese ambassadorial coaches are so absurdly gilded and enormous that the room is genuinely funny.

Eat a custard tart before you leave. The bakery near the monastery has been making them to a monastery recipe since 1837 and there is always a queue for the counter and rarely one for the tables inside.

Take a late morning train from Sete Rios. It crosses the 25 de Abril bridge, the same colour as the Golden Gate and built by the American company behind the Bay Bridge, and then runs down the peninsula for another half hour. Fifty minutes in total, and you arrive in a town that has no idea it is on anybody's itinerary.

Go straight to the Livramento market. It is a covered hall whose walls are lined with azulejo panels of fishermen, boats and the catch, and underneath them is the actual catch, laid out on ice by people who shout. It closes in the early afternoon, which is why this is the first thing rather than the second.

In the afternoon walk or take a taxi up to the Castelo de Sao Filipe, a star fort built above the town by Philip II of Spain in the 1590s to hold the Portuguese down after he took their crown. The chapel inside is tiled floor to ceiling and the terrace looks straight down the Sado to the sand spit at Troia.

Then eat cuttlefish. Choco frito, fried in strips with lemon, is Setubal's dish and every tavern in town does it.

The boats leave from the marina in the morning and go out into the estuary for about three hours. There are somewhere around thirty resident bottlenose dolphins in the Sado, one of the very few estuary populations in Europe, and the operators work under permit with distance rules, so nothing chases anything. Sightings are usual rather than guaranteed. Take a jumper: it is colder on the water than the town suggests.

In the afternoon go over the Arrabida ridge. The road climbs out of Setubal into a limestone range covered in maquis and drops to a coast of small white beaches and water that is a completely different colour from the open Atlantic ten kilometres west. The viewpoint above Portinho da Arrabida is where to stop, and the beaches below it are where to stay if the day is warm.

Finish inland at Azeitao. Jose Maria da Fonseca has been making wine here as a family since 1834, the cellars hold barrels of Moscatel de Setubal older than anybody visiting, and the tour ends with a tasting of a fortified wine that most people have never had and that goes with almost any pudding. Book the slot in the morning.

This is the long train day and it is worth doing in daylight. Change at Pinhal Novo, run south through the Alentejo cork country, change again at Tunes, and reach Lagos in about four and a half hours. Buy something to eat before you start.

Lagos is small and the first thing to do in it is the hardest. The Mercado de Escravos on the Praca Infante Dom Henrique is where, in 1444, Europe's first market for enslaved Africans was held, and it is now a museum that says so plainly, in a town that has every commercial reason to be quiet about it. It takes half an hour and it changes how the rest of the afternoon reads.

Then out to the Forte da Ponta da Bandeira on the point, a small seventeenth century fort guarding the harbour mouth, and down to Praia da Batata directly below it, which is a proper beach two minutes from the old town with cliffs at one end and a tunnel through the rock to the next cove.

Eat in the lanes behind the market. Cataplana, the copper pot of clams and pork or fish, is the thing to order and takes two people.

Go west. The bus from Lagos to Sagres takes about an hour along the bottom of the country; the cape is another six kilometres beyond the village, with a shuttle in summer and taxis the rest of the year. A hire car for the day makes the whole thing easier and lets you stop at the beaches on the way.

The Fortaleza de Sagres occupies a flat promontory sticking into the Atlantic, walled across its neck, with a huge stone compass rose laid into the ground inside. Henry the Navigator is supposed to have run a school of navigation here, which historians have been quietly demolishing for a century, but he did live on this headland and the voyages did leave from this coast. Whatever the truth, standing on the cliff edge with the swell coming in from three sides explains more than any museum.

Six kilometres further is Cape St Vincent, the southwestern corner of Europe, with a lighthouse on the point and seventy metres of cliff straight down into the sea. It is the last land until America and it feels like it. There is a sausage van in the car park that has been there for decades and calls itself the last bratwurst before America.

Back in Lagos for the evening, walk out to Ponta da Piedade, twenty five minutes along the clifftop, where the sandstone has been cut into stacks and arches and there are steps down to the water. Sunset is the point.

One coach, about five hours, from Lagos through the eastern Algarve, over the Guadiana and across the flat empty country behind Huelva. There is a stop halfway. Remember that Spain is an hour ahead, so you arrive later than the ticket appears to say.

Seville in the late afternoon is a good introduction because nothing is open and nobody minds. Walk to the Metropol Parasol, which everyone in the city calls the mushrooms: an enormous timber lattice on stilts over a square in the old town, finished in 2011 to a German architect's design, with a walkway across the roof of it. Go up for the last of the light, which puts the cathedral and the whole roofscape at eye level.

Then north to the Alameda de Hercules, a long tree-lined square with two Roman columns at one end that were dragged here from a temple in the 1570s. It is where Seville drinks, it is not a tourist quarter, and the tapas bars around it are better and cheaper than anything near the cathedral.

Do not plan dinner before nine thirty. You will be the only people in the room.

Take the first slot at the Real Alcazar, booked weeks ago. What you walk into is a Mudejar palace built for Pedro I in the 1360s inside an older Almohad fortress, decorated by Muslim craftsmen for a Christian king, and then added to by every dynasty since, so the plasterwork is Granadan, the tilework is Sevillian and the upper floors are still an official royal residence. The gardens at the back are as good as the rooms and much emptier.

The cathedral is two minutes away and is the largest gothic church in the world by volume, built deliberately enormous on the footprint of the great mosque. The Giralda beside it was that mosque's minaret, with a Renaissance belfry dropped on top; you climb it by ramps rather than stairs, because it was built for a man on horseback. Columbus is in a tomb held up by four pallbearers, and whether all of him is in there has been argued about ever since.

Finish across the square at the Archivo General de Indias, in the sixteenth century merchants' exchange. It holds the paperwork of the Spanish empire in the Americas, some forty three thousand files, and the reading room and the shelving are the exhibit. It is free and it takes half an hour.

Then get out of the monumental centre for dinner.

Seville built itself a world's fair in 1929 and then kept the buildings, which is why the south of the city looks like nowhere else in Spain. The Plaza de Espana is the centrepiece: a semicircle of brick and tile two hundred metres across, with a canal in front of it, bridges over the canal, and a tiled alcove for almost every province in the country set into the wall. It is free, it is open, and it is at its best before ten in the morning.

Behind it, the Parque de Maria Luisa was the exhibition's gardens and is now the city's, full of tiled benches, ponds, doves and enough shade to survive a July afternoon in. Walk it slowly to the far end, where two of the remaining pavilions house the archaeological museum.

Rest through the middle of the day, because the evening is the point. Go to a small flamenco room rather than a dinner show: no meal, no castanets, a hundred seats, and three performers who take it seriously. The good ones run at seven and nine and sell out the same day.

Eat afterwards, at eleven, like everyone else.

One last thing before the airport, and it should be indoors and small. The Casa de Pilatos is a private palace begun around 1500 by a family who had been to Jerusalem and came back with ideas, and the result is the best example in Seville of what happened when Italian Renaissance and Mudejar craft were used on the same building at the same time: Roman statues in a tiled courtyard under a plasterwork frieze.

It is still owned by the Medinaceli family, the upper floor is only shown on a guided visit, and the ground floor and gardens on their own take about an hour. It is ten minutes' walk from the cathedral and almost nobody is in it.

Then the airport, which is fifteen minutes out by bus from the Plaza de Armas or by taxi from anywhere in the centre, or Santa Justa station for the high speed line north.