The Retiro is the green heart Madrid retreats into — the old royal pleasure-grounds, opened to the city, and now the place every madrileño claims as their own back garden. Do it in the afternoon and let the light do the work.
A little over four kilometres, gentle throughout. From the Retiro Metro, enter by the Puerta de Felipe IV and head for the Estanque Grande, the boating lake under the bronze king on his colonnade — hire a rowing boat or just watch from the steps. South to the Palacio de Cristal, the glass pavilion floating over its pond, free to enter and reason enough on its own; the brick Palacio de Velázquez nearby is its quieter sister.
Then the gardens proper: La Rosaleda, the formal rose beds, loveliest in May. You don't have to time it; the shape holds all year.
Finish at the Fuente del Ángel Caído — a fountain topped with the falling Lucifer, one of the rare monuments anywhere to the Devil himself. Leave by the south gate and walk down to Atocha.