Now you've got the essential lay of the land, having spent your first day in Madrid as outlined in the one-day itinerary. Use your second day as an opportunity to combine some leisurely wanderings among Madrid's top green areas — from the illustrious Retiro to the huge Casa de Campo — with a peek at farther cultural spots large and small, from the great Royal Palace that once housed kings to the tiny chapel where Goya is buried. And you'll get the chance to discover what radical changes — in the form of new walkways and gardens — the capital has carried out along the banks of its once tiny and ignored Manzanares River.

Start: Metro: Retiro. Bus: 15, 146

1. Parque del Retiro

Start with an early breakfast and a stroll among the joggers and tai chi exercisers as far as the Estanque (lake) in Parque del Retiro. Once the prerogative of royals alone, this rectangular oasis of greenery has become a popular rendezvous for residents ever since it was opened up to the public in 1868.

2. Museo Thyssen-Bornemisza

More exquisite art if you're game. This superb, multifaceted gallery, founded by the now defunct Baron Hans Heinrich and his wife, Carmen "Tita" Rivera, also has an impressive extension for temporary exhibitions. To get a rough idea of the museum's vast range, peep first at the Old Dutch masters and then at modernist masterpieces by Klee, Braque, and Picasso.

3. Cibeles

Madrid's most famous fountain lies at the meeting point of Alcalá and the Paseo del Prado, opposite the Banco España and main post office (Palacio de Comunicaciones). Sporting successes are traditionally celebrated with great enthusiasm in this square. When Spain defeated Holland to win the World Soccer Championship in Johannesburg in July 2010, the huge city fiesta that culminated here was the most extravagant and noisy even this lively city has seen, way superceding the shindig two years earlier when the national team beat Germany to win the UEFA Champion's League European Cup.

4. Círculo de Bellas Artes

This Art Deco gem has exhibitions in various salons as well as an adjoining excellent value cinema and an iconic ground floor cafe. You can also pop up to the top floor and look at the library, even if you're not a member.

5. Take a Break — Círculo de Bellas Artes

The Círculo de Bellas Artes' spacious and well-worn cafe evokes a turn-of-the-20th-century aura, with its chandeliers, recumbent statue of a naked lady, and high wide windows overlooking the junction of Alcalá and the Gran Vía. TV morning interviews with established and up-and-coming politicians alike are often held against this backdrop, so you might get a glimpse of some future Spanish president.

6. Real Academia de Bellas Artes de San Fernando

Time for a quick peep at another unmissable temple of art, located just up Alcalá on the way to Puerta del Sol. This one's the oldest in Madrid and remarkable for its wealth of Spanish and Dutch masters. See the roomful of Goyas if nothing else. 

7. Monasterio de las Descalzas Reales

An oasis of calm in the midst of the urban mayhem, this 16th-century convent seems hundreds of kilometers from Madrid instead of just a stone's throw from the Gran Vía — though there is admittedly a slight sense of rush as you "do" the array of corridors and paintings in around 20 minutes. Some of these guided visits only have commentary in Spanish, so bring along an architectural guide book, if you've got one, to be on the safe side. 

8. Take a Break — Casa Ciriaco

After this surfeit of culture, tuck into a satisfying lunch at one of Madrid's remaining genuinely traditional eating spots, Casa Ciriaco. Photos of eminent historic figures line the walls; pre-'30s radical thinkers used to meet here to put the world to right. Before the building became a restaurant, antiroyalists once threw a bomb at Alfonso XIII from one of the balconies. (He was unharmed, though many others were less fortunate.) These days, the mood is neither anarchic nor intellectual, but the hearty Castilian food is great nonetheless. 

9. Palacio Real

A Bourbon monument of granite and white stone, this vast Italian-designed 18th-century palace is one of Madrid's greatest architectural assets. Though it's not used much by today's royal family, official ceremonies are often held here, so best to check before your visit to make sure it's open. Fifty of its near 3,000 sumptuous salons are accessible to the public. If you come at noon on the first Wednesday of the month (excluding January, August and September), you'll catch the colorful changing of the guard.

10. Almudena Catedral

Built over an unbelievably protracted period of 110 years — during which time its originally projected Gothic style eventually gave way to one of neoclassicism — this bright, but rather vacuous, 20th-century creation pales in comparison with the 11th-century mosque that long preceded it. It's worth a look for its 16th-century image of the Virgin of the Almudena in the crypt, the polychrome funeral casket of San Isidro, and the controversial abstract stained-glass windows, which provide some welcome color.

11. Parque de las Vistillas

Located at the southern end of the Puente de Segovia viaduct, close to the secretive Capilla del Cristo de los Dolores, this tiny area of parkland offers some of the best views in the city. Below you lies the green expanse of the Casa de Campo, while over to the northeast, you can see the distant purple-grey range of the Guadarrama Mountains, snow-capped in winter. During the San Isidro and Virgen de la Paloma fiestas, lively verbenas (fairs) held here fill the night air with music.

12. Campo del Moro

Though the name has 11th-century Moorish connotations (when the city was under siege), the charming Campo del Moro is in fact laid out like a rather lush English park. Designed in 1844 and first opened in 1931, it was closed during the Franco Era and finally reopened to the public in 1983. Today you can stroll at leisure among the flower beds, lawns, and fountains and enjoy the marvelous view of the Palacio Real towering above.

13. Ermita de San Antonio de la Florida (Panteón de Goya)

Halfway along the Paseo de la Florida, which runs parallel to the Manzanares River, you'll find this delightful domed hermitage — the right-hand one of an identical couple. Some of Goya's most evocative frescoes (beautifully restored in 1996) depict the Miracles of Saint Anthony on the interior of the cupola. The artist himself is buried in front of the altar.

14. Casa Mingo

A great place for sampling cider — still or fizzy — and stuff cooked in it like delicious, calorie-loaded chorizo, Casa Mingo is a mere stone's throw from the Ermita de San Antonio de la Florida. This used to be a popular student hangout, and though it's not so cheap these days and sees a lot more tourists than students, it's still great fun — either inside under the rafters and beside the barrels or outside on the roof on hot summer evenings.

Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.