Madrid, Spain

Day 1

• Plaza Mayor

  A public square, free and always walkable: what you pay for are the tables under the arcades, at the highest prices in the centre. It was closed on all four sides in the 17th century and rebuilt three times after as many fires, the last by Juan de Villanueva, the same architect as the Prado. The bars where you eat the calamari roll are not on the square but on the streets that wrap around it, towards the Cava de San Miguel: same thing, half the price.

• Royal Palace (Palacio Real)

  Eighteen euros, nine reduced, twenty-four with the Galería de las Colecciones Reales. Capacity is limited and box-office sales are cut back: buy online. Monday to Thursday the last two hours are free (4-6pm October to March, 5-7pm April to September), with last entry an hour before. The changing of the guard is watched free from outside on Wednesdays and Saturdays from 11am to 2pm (10am-noon in July and August), and on the first Wednesday of the month at noon there is the solemn relief, with horses and band. The Campo del Moro gardens are free.

• Prado Museum

  Fifteen euros, €7.50 reduced, free for under-18s and for students between 18 and 25. The last two hours before closing are free (6pm to 8pm Monday to Saturday, 5pm to 7pm on Sundays), but those tickets are only handed out at the desk and run out once capacity is reached: there are none online. Entry runs on a timed pass and closes 30 minutes before the end. The €32.80 Paseo del Arte pass lasts a year and also covers the Reina Sofía and the Thyssen: it pays for itself on the second visit.

Day 2

• Reina Sofía Museum

  Twelve euros, and it is closed on Tuesdays, not Mondays like almost every European museum: the mistake that wastes the most afternoons in Madrid. Entry is free from 7pm to 9pm on Mondays and Wednesday to Saturday, and on Sundays from 12.30 to 2.30pm, but you still need a ticket, which can be booked online. Guernica is on the second floor of the Sabatini building; anyone who already has an online ticket gets in faster through the Nouvel building on Ronda de Atocha.

• Retiro Park

  A hundred and fourteen free hectares, open 6am to midnight from April to September and 6am to 10pm from October to March; on days of strong wind the city closes it outright, and that happens more often than you would think. Rowing boats are hired on the lake. Watch out for the Palacio de Cristal: it is temporarily closed for building works, and guides still list it as a stop. When open, like the Palacio de Velázquez, it is free to enter.

• Gran Vía

  Opened in 1910 and finished in 1931, it was a surgical cut through the old city: dozens of streets vanished to make room for it. Today it is the musicals street: the historic theatres run the same production for years, with weekday matinees far cheaper than evening shows. It is also the axis where pickpocketing concentrates, because it is the one place in Madrid where everyone walks looking upwards.

Day 1

• Lavapiés district✦ hidden gem

  The district with the highest share of foreign-born residents in the city, immediately south of Sol. The centrepiece is the Tabacalera, the old tobacco factory on calle Embajadores: one part is a self-managed social centre covered in murals, the other holds photography exhibitions with free entry. Around it, Bangladeshi and Senegalese restaurants and the fringe theatres. It is also El Rastro's neighbourhood, so on Sunday mornings it changes face completely.

• El Capricho Park✦ hidden gem

  The detail that wrecks the trip: it opens only on Saturdays, Sundays and public holidays, 9am to 9pm from April to September and until 6.30pm from October to March. Entry is free. It is an 18th-century garden commissioned by the Duchess of Osuna, with a lake, a temple and a maze; beneath it lies the bunker of Posición Jaca, a Republican command post from the Civil War, visitable on free guided tours by booking, in groups of twenty.

• Carabanchel and the murals of Madrid's Soho✦ hidden gem

  A former industrial district south of the centre, today the area with the highest concentration of contemporary art galleries in Madrid, installed in the disused warehouses. It is not a walk to improvise: the galleries keep office hours and close at the weekend, so it is worth checking what is open first. The large-format murals, on the other hand, are seen from the street at any hour. Metro line 5, Oporto or Vista Alegre.

Day 2

• Usera, Madrid's Chinatown✦ hidden gem

  This is Madrid's Chinatown, on the south bank of the Manzanares, on metro line 6 (Usera stop) or line 3. The restaurants here do not do the adapted version: you find distinct regional kitchens (Sichuan, Zhejiang, Cantonese) and the menus often have a section written only in Chinese. At Lunar New Year the district hosts the city's biggest parade. It is off the tourist routes and the prices say so.

• Templo de Debod✦ hidden gem

  An Egyptian temple from the 2nd century BC, taken apart stone by stone and given to Spain in the 1970s for its help rescuing the Nubian temples threatened by the Aswan dam. Entry is free but only thirty people are let inside at a time, so there is a queue; it is closed every Monday, public holidays included, and opens Tuesday to Sunday 10am-8pm (until 7pm from 15 June to 15 September). The sunset, though, is watched from outside: that has neither queue nor opening hours.

Day 1

• Usera, Madrid's Chinatown✦ hidden gem

  This is Madrid's Chinatown, on the south bank of the Manzanares, on metro line 6 (Usera stop) or line 3. The restaurants here do not do the adapted version: you find distinct regional kitchens (Sichuan, Zhejiang, Cantonese) and the menus often have a section written only in Chinese. At Lunar New Year the district hosts the city's biggest parade. It is off the tourist routes and the prices say so.

• Cocido madrileño

  It is eaten in three courses and in this order: first the broth with fine noodles, then the chickpeas with the vegetables, then the meats. Asking for it all at once is considered a mistake. It is a winter dish that needs hours of cooking, so many old taverns make it only on certain days of the week and some want it ordered the day before: better to phone than to turn up and hope.

• Bocadillo de calamares

  Madrid has no sea but it has Mercamadrid, one of the largest fish markets in Europe, which is why the city's signature sandwich is fried calamari. Order it in the bars around Plaza Mayor, not under the arcades: it costs half. It arrives bare, without sauces (lemon yes, mayonnaise is a concession to tourists) and it is eaten standing at the counter, as almost everything is here.

Day 2

• Madrid-style tortilla de patatas

  In Madrid it is served tall and still runny in the middle: if it arrives compact and dry, it is overcooked. The question that divides the country is 'with or without onion', and bars write it on the blackboard. It is ordered as a tapa alongside the house beer, the caña, which is a small glass precisely so it stays cold: asking for a large beer in a tapas bar is the quickest way to drink it warm.

• Mercado de San Miguel

  Open every day from 10am until midnight, and until 1am on Fridays, Saturdays and the eve of holidays; going in costs nothing. The iron-and-glass structure is from the early 20th century and the market was a wholesale one: today it is a couple of dozen food counters taking seven million visitors a year. Which is also the problem: you eat standing, packed in, at old-town prices. It works as a quick taste, not as dinner.

• El Rastro

  It is held on Sundays and on public holidays, not only Sundays, from 9am to 3pm, with the stalls going up from 8am and coming down right after 3pm. Its heart is plaza de Cascorro and Ribera de Curtidores, in the Embajadores district. On weekdays the stalls are not there, but the area's antique shops and galleries stay open: that is how to see the same things without the crush.