On a budget, Museo del Prado still earns its price.
€15 (free Mon–Sat 18:00–20:00, Sun 17:00–19:00)
One of the three or four greatest painting collections on earth, and Las Meninas alone justifies the trip. The catch is scale and density — it's overwhelming in one go, and the free evening window (Mon–Sat 18:00–20:00) packs the rooms shoulder-to-shoulder, so first thing in the morning is the calm play.