Ten days in Spain: From Mediterranean Light to Andalusian Heat by Rail

The promenade from Plaça de Catalunya down to the sea, and the line everybody navigates by. Walk it once and then eat elsewhere: prices on it are roughly double what they are one street back, and it is the most worked pickpocket ground in Spain.

The Gothic cathedral of Santa Eulàlia, 14th and 15th century with a 19th century front. Go for the cloister rather than the nave: orange trees, a fountain, and thirteen white geese kept for the thirteen years the city's martyr was said to have lived.

An arcaded square of palms and yellow stucco a few steps off the Rambla, laid out from the 1840s where a convent had stood. The lamp posts with the winged helmets were an early commission of Gaudí's, in 1879, when he was fresh out of school.

The lanes around Plaça Sant Jaume fill from nine. Two turnings from the Rambla is the line between a menu with photographs on it and one without.

Started in 1882, handed to Gaudí a year later, and unfinished when a tram killed him in 1926. The eastern front is the part he built himself and repays ten minutes outside before you go in. The interior is a stone forest with coloured light falling through it, cool at one end of the day and hot at the other.

Twelve minutes up the avenue, and the quietest great building in Barcelona: a hospital laid out as a village of tiled pavilions by Domènech i Montaner, linked by tunnels so nobody crossed the gardens in the rain. It was still treating patients in 2009.

The pedestrian street between the two buildings is lined with terraces, and it is the one place near the basilica priced for the neighbourhood rather than the queue.

Gaudí's 1906 remodelling of an ordinary apartment block: a bone-coloured front, a scaled roof, and a light well tiled dark at the top and pale at the bottom so daylight reaches the ground floor evenly. Book it, and go late in the day when the tour groups thin out.

A housing estate that failed, laid out by Gaudí from 1900 for a developer who managed to sell almost none of the plots, and left as a park instead. Two gatehouses like something from a fairy tale, a mosaic lizard on the steps, a hall of leaning columns and a bench of broken tile winding around the terrace above.

The neighbourhood below the park is a village the city grew around, with small squares full of terraces and prices that have not entirely caught up.

Five joined medieval palaces holding the fullest account anywhere of Picasso before he was Picasso: teenage academic paintings made in this city, the blue period, and 58 canvases from his 1957 argument with Velázquez. Closed on Mondays.

Four minutes away, and the corrective to a week of ornament. Built between 1329 and 1383 by the parish of sailors and porters, it is Catalan Gothic stripped bare: three near-equal aisles, columns set unusually wide apart, and almost nothing on the walls since a fire in 1936.

Two hours thirty by high speed train, over 600 km of purpose-built line. Be at Sants half an hour early for the luggage scan, and book weeks ahead: three operators run the route and the early fares are a fraction of the late ones.

The square the country measures itself from: a slab in the pavement outside the old post office is kilometre zero for the six main roads of Spain, and the clock above it is the one the whole country watches on New Year's Eve. The bronze bear at the strawberry tree is the city's arms and everyone's meeting point.

Five minutes southwest, a closed rectangle of red facades finished in 1619 with nine archways cut through them. Markets, bullfights and executions have all happened on this paving. The painted building on the north side was the bakers' guild hall.

The avenue driven diagonally through the old streets between 1910 and 1929, and the reason Madrid has a skyline. Walk it at dusk from the Alcalá end, past the cinemas and the 1920s towers with the signs coming on. Free, loud, and better than most paid attractions.

The lanes below Plaza Mayor are wall to wall bars. One plate and one small beer at each of a few of them is the method, and nothing starts before half past nine.

The Prado, opened in 1819 from the royal collection, and the reason art historians come to Spain. Start with Velázquez, then the Goya rooms downstairs, and let the Italians go. Las Meninas is worth twenty minutes on its own. The Thyssen collection across the road fills the gaps the kings left, if two galleries in a morning appeals.

Two streets west of the boulevard the prices drop by a third and the set lunch appears. It is the right length of break between two very different galleries.

Ten minutes south, in an 18th century hospital with glass lifts stuck to the outside. Guernica is here, painted in Paris in 1937 and kept out of Spain until 1981, and the room of studies around it is what makes it land. Dalí and Miró upstairs. Shut on Tuesdays.

Uphill into the old royal garden, laid out in the 1630s and given to the public in 1868: rowing boats, a glass pavilion built in 1887 for a display of Philippine plants, and on Sunday evenings a drum circle that has outlasted several generations. The last hour before dark is the good one.

Begun in 1738 after the old fortress burned down on Christmas Eve 1734, and enormous: more than 3,000 rooms, of which the tour covers perhaps twenty. The Tiepolo ceiling in the throne room and the porcelain cabinet are the two nobody forgets. No monarch has lived here since 1931.

The streets between the palace and the Teatro Real are full of ordinary places at ordinary prices, which after the palace floors is exactly what is wanted.

The Royal Academy of Fine Arts on Calle de Alcalá, five minutes from Sol, where Goya was once director of painting and Picasso lasted a few months as a student. A whole room of Goyas including the self-portrait, cheap to get into, and usually near empty.

A 2nd century BC Egyptian temple, given to Spain in 1968 for its part in rescuing the Nubian monuments from the water rising behind the Aswan dam, and rebuilt block by block on this ridge. Free, capped at thirty people inside, and the reason to come is what happens behind it as the sun goes.

Two hours twenty on the fastest services, along 470 km of track that opened in 1992. Departures run roughly hourly. Santa Justa is fifteen minutes on foot from the centre, or a few minutes by bus or taxi.

A timber lattice the size of a city block, finished in 2011 and known to everybody as the mushrooms. A lift takes you to a walkway that winds above the rooftops, and the ticket includes a drink up there. Go for the last hour of daylight.

Opened in 1670 and generally called the oldest tavern in the city: hams overhead, no menus on the tables, and the bill chalked on the wooden counter as you order. Spinach with chickpeas, and salmorejo, standing at the bar.

A room in Santa Cruz with a singer, a guitarist and a dancer, close enough that the floor is part of the sound. An hour, no dinner, several shows a night, and nothing like the coach-party version. Book it the same afternoon.

Begun by the Almohads in the 12th century and rebuilt in the 1360s for Pedro I by Muslim craftsmen working for a Christian king. Plasterwork like lace, tiled walls, still pools and orange courtyards, then gardens that go on much longer than expected. The upper floor is still the royal family's Seville residence.

The merchants' exchange of the 1580s, turned in 1785 into the archive of Spanish America: shelf on shelf of the empire's paperwork along the whole upper floor, with Columbus's own journal among it. Free, cool, and never crowded.

Two streets north of the cathedral the prices halve. The test is simple: a queue of people speaking Spanish at half past two is a good sign, a photograph of paella is not.

Built between 1401 and 1506 on the footprint of the great mosque, and the largest Gothic church in the world by volume, its central nave 37 metres up. Columbus is buried inside, carried by four kings. The tower is the old minaret of the 1190s with a Renaissance belfry on top, climbed by shallow ramps built for a man on horseback.

A brick and tile crescent 200 metres across, built as the host pavilion of the 1929 Ibero-American exhibition, with a tiled alcove for every province of Spain along the base of it. Find yours. It has played Naboo in Star Wars and Cairo in Lawrence of Arabia, and it is free at any hour.

The gardens behind it, given to the city in 1893 and landscaped for the same fair: ficus roots like walls, tiled benches, ponds and two exhibition pavilions that are now museums. The deepest shade in the city and the reason this day works in July.

Eat near the old tobacco factory at the top of the park, then do what Andalusia does between three and six, which is to be somewhere shaded with no plans at all.

A twelve-sided Almohad watchtower on the bank, put up around 1220 to hold one end of a chain across the river and shut the port. There is a small naval museum inside and the roof gives you the bend of the Guadalquivir with Triana opposite. Cross the bridge afterwards.

A 16th century palace built by a family fresh back from Jerusalem, which is where the name comes from, and the best Mudéjar courtyard in Seville outside the Alcázar: tiled to shoulder height, Roman statues in the corners, a fountain in the middle. The upper floor is a separate guided ticket and the family still uses it.

Fifteen minutes on foot to Santa Justa, or five in a taxi. Anywhere on the Alameda has a terrace and nobody in a hurry.