Museo de San Isidro is a compact local history museum in La Latina, built around Madrid before it became the capital. One side covers Saint Isidore the Laborer, the city's patron saint; the other follows the archaeology and paleontology of the Madrid region from prehistory to the court of Philip II.
It is a useful stop if you want Madrid's older layers, not just the Bourbon palaces and Prado axis. Most exhibits have Spanish and English explanations, so it works well as a short, focused museum between walks through La Latina.