The Prado is free 18:00–20:00 daily (Sun 17:00–19:00); the Reina Sofía most evenings 19:00–21:00 and Sunday afternoons; the Thyssen Mondays 12:00–16:00. Add the permanently free ones: CaixaForum’s exhibitions-lobby and vertical garden, the Museo de Historia de Madrid, CentroCentro in the Cibeles palace (plus its free viewpoint floor), and the house-museums’ free windows — Sorolla Saturday afternoons, Romanticismo likewise. Seen properly, Madrid’s entire first division of art costs zero if you plan the week around the windows.
The Retiro, the Botanical Garden’s exterior avenues, Madrid Río’s ten riverside kilometres, Casa de Campo’s 1,700 hectares, and the Templo de Debod at sunset — the single best free moment in the city. Add the Sabatini gardens and the Campo del Moro under the Palacio, and Las Vistillas for the Guadarrama horizon. None of it costs a cent at any hour.
El Rastro (Sundays 9:00–15:00) is five centuries of flea market and the city’s best free theatre. The changing of the guard at the Palacio Real is free Wednesdays and Saturdays (the full cavalry version, first Wednesday monthly). Gran Vía’s architecture, the brass literary quotes underfoot in Huertas, Malasaña’s murals, Chueca’s market bustle, and the Christmas lights in season — the city itself is the exhibit.
Free walking tours leave Plaza Mayor daily (tip-based, book online). And the cheapest great view in Madrid: the Círculo de Bellas Artes rooftop costs a few euros, but the Cibeles palace mirador is nearly free and the Vistillas gardens entirely so.
The sierra is a free attraction reached with a transport card: the Fuenfría Roman road, the Purgatorio waterfalls, Manzanares el Real’s river pools and every viewpoint in this site’s walks hub. Alcalá’s Cervantes birth-house museum is free; Buitrago’s Picasso collection is free; the storks are free everywhere.
Curated picks are coming — meanwhile, the live search covers every bookable property at the same price or better.