Start your day the Madrileno way with a cafe con leche and a napolitana (a kind of custard pastry) at the bar of La Mallorquina - a Madrileno institution on the corner of the Puerta del Sol. Cross the road to the town hall and look for the inconspicuous plaque set into the pavement which marks Kilometro Cero.
If in Italy all roads lead to Rome, in Spain they all end up here. This is the spot from which road distances to the capital are measured; it's the symbolic centre of the city and near enough the middle of Spain.
Madrid owes its present eminence to the whims of a king. Felipe II moved his court here from nearby Toledo in 1561, partly because its geographical position appealed to the eccentric monarch's love of geometry. As a consequence of its late development, the city does not have the ancient aura or architecture of other Spanish cities. But take a stroll down Calle de Alcala, to your right, and efforts to inject some civic pride are much in evidence.
Elegant, turn of the century buildings - such as the grand 1920s exterior of Circulo de Bellas Artes, Madrid's cultural headquarters - line this broad throughfare, but are nothing compared to the sight that greets you at the bottom of the hill.
The Palacio de Comunicaciones in Plaza de Cibeles is probably the most wonderful post office in the world. It's an art nouveau extravaganza with marble floors, a sweeping staircase and huge revolving doors. Go in to buy a stamp and you'll come out feeling like a film star.
Emerge on to Paseo del Prado. To the north, on Paseo de Recoletos, modern office buildings dwarf the few remaining villas. But walk south along Prado's broad, shaded pavements and parks and you get some idea of the former grandeur.
You are now entering the so-called "golden triangle" - an area with one of the highest concentrations of art treasures in the Western World - where three great museums (the Prado, Thyssen and Reina Sofia) stand within a few hundred yards.
Just past the Prado, take a detour into the botanical gardens on the left. Built in 1781 and hardly changed, they are a little oasis of calm. You'll be glad you did when you arrive at Glorieta Emperador Carlos V, a manic high-speed road junction. Take your life in your hands and cross the road to Atocha railway station.
In the early 1990s the original station - a classic wrought iron and glass arch - was converted into a giant tropical greenhouse and a new station was added on the back, to accommodate the AVE high-speed train link to Seville.
Coming out of the station and looking over the road you will see the twin transparent lift shafts of the Reina Sofia museum. This is another building that has been reinvented, from 200-year-old hospital to contemporary art museum whose most famous exhibit - Picasso's Guernica - is alone worth the entrance fee.
Leave the tourist trail behind now and head up the hill along Calle de Santa Isabel. This is Lavapies, one of the oldest parts of town and a good place to soak up some local atmosphere. Stop for lunch in one of the many restaurants or bars along Santa Isabel where you can find a menNo del d!a - three courses plus wine - for under a fiver.
At the Filmoteca (Madrid's beautifully restored 1920s art cinema) turn left down Calle del Olmo, which runs across the hillside past narrow, picturesque streets that descend to the small Plaza de Lavapies.
Turn right into the triangular Plaza Tirso de Molina, down the road on the opposite side of the plaza - Calle de la Colegiata - until you meet Calle de Toledo. The tall arch to your right leads into the Plaza Mayor, a vast cobbled square that in its time (more than 500 years) has seen everything from executions to bullfights, Christmas fairs and world record-breaking paella making. The Plaza Mayor is a favourite siesta time hangout for people with no homes to go to.
So while the locals head for their beds, and students loll around the cloisters, the tourist thing to do is retire to a place in the shade at one of the square's many terrace cafes and contemplate a cana.