Check this page out for some sites you must see.
Catedral Santiago de Compostela:
World-renowned pilgrimage and World Heritage site, the cathedral of old town Santiago de Compostela is not only architecturally stunning but is steeped in history. Walk around the city of Santiago to find great restaurant and authentic artisanal shops.
Plaza de María Pita:
Located at the Center of A Coruña is the Plaza de María Pita. It’s filled with Pulpo (the region’s famous octopus dish) resturants, tourist shops, and the Paseo Maritimo which is a path along the city’s coast.
City of Lugo:
You must Visit the city of Lugo which is famous for its ‘La Muralla de Lugo‘ which is a ancient Roman wall that runs around the city and allows you one of the coolest walks you will take in Galicia.