The Pilgrimage Museum gives useful depth to Santiago de Compostela's most obvious story. Rather than treating the Camino as a souvenir trail, it explains pilgrimage as a religious, social, artistic, and economic force that shaped the city for centuries.
It is especially worth visiting before or after the cathedral, when the scallop shells, routes, relics, and pilgrim rituals are fresh in your mind. The museum is compact enough to fit into a central walk, but substantial enough to change how you read the old town.