Madrid for a tourist is actually rather easy to walk. Other than for a
business trip, it is unlikely you will travel in the northern parts of the
city, except to catch a football (soccer) game at Bernabeu Stadium. Other
than that, you can walk from the main sights in a rather manageable area
between the Palacio Real (Royal Palace) and the gardens of El Retiro. The
three great museums - the Prado, Reina Sofía and Thyssen-Bornemisza - are
conveniently located on a street called the Paseo del Prado, not far from
Retiro Park. The oldest part of the city encircles the beautiful Plaza
Mayor, a five minute walk from the Palacio Real.
If you aren't planning to spend much time in Madrid, you should stick to the
main tourist areas of Madrid, enjoying the street life. Each neighborhood
has it's own feel and you'll be handsomely rewarded for your sense of
adventure. The best advice is to wander -- stop at a pastry shop, grab a
beer or wine at a local bar, explore a shop that no one else is visiting.
The central area is also the most rewarding -- around Plaza de Santa Ana and
c/Huertas, from the Royal Palace to Puerta del Sol and on to Atocha Train
Station. Plaza Mayor and south will show you one of my favorite areas; La
Latina and Lavapiés -- perfect for the Sunday market, El Rastro; Malasaña
and the gay neighborhood Chueca, north of Gran Vía. Drink, eat and relax
--these areas have some of Madrid's finest tapas bars, restaurants and
shops.