As a former student of the local university, I had been many times to the cathedral but being up on the roof showed me a lot of things I didn't know about the cathedral.
They will take you to the cathedral stone roofs (don't wear high heels!), where you get great views of the old city.
www.santiagoturismo.com/
€10 for 30-45 minutes, everyday 10am to 2 pm, 4pm-8pm. Booking recommended (especially in summer), entry via Pazo de Xelmirez, Praza do Obraodiro.