The Contemporary Art Centre of Galicia, usually shortened to CGAC, is Santiago's main contemporary art museum. Its exhibitions focus on modern and contemporary work from Galicia, Spain, and abroad, and the programming changes often enough that it is worth checking what is on before you go. It is a useful reset after the cathedral circuit: white galleries, clean lines, and present-day arguments instead of carved granite saints.
The building is part of the reason to visit. Portuguese architect Álvaro Siza set the museum beside the convent of Santo Domingo de Bonaval, using pale stone and restrained geometry that sits quietly against the old city rather than shouting over it. Pair it with the neighbouring Bonaval park and the Museo do Pobo Galego for a good half-day just outside the most crowded lanes.