The Catedral del Apostolo is the main point of interest in Santiago de Compostela, but the surrounding monuments are also worth noting. Each facade of the massive Baroque church faces a plazas; the Catedral's south door opens into the Praza das Praterias (Plaza de las Platerias). The centerpiece of this square is a large fountain, La Fuente de los Caballos, a sculpture of four spirited horses with webbed feet.
Fantastic equestrian statuary aside, this plaza is also known as "the silversmith's plaza," and indeed, the arcades on the perimeter are occupied with vendors selling silver goods and trinkets. These little shops are what distinguish the Plaza de las Platerias from the others, but the narrow streets of the Old Quarter (the part of town built around the Catedral) radiate from the Catedral and its plazas, and you can find more shopping and vendors in these charming alleys.
In particular, south of the Cathedral and the Plaza de las Platerías is the old town of Santiago, centered on two parallel streets, Rúa del Villar (with the 18th-century Casa del Deán at its near end, on left) and Rúa Nueva (Galician Nova). On these two streets, you'll find bars, restaurants and souvenir shops.
The Old Town (or Old Quarter, if you prefer) has plenty of shopping and eating, but much of Santiago's cultural input comes from the University, found in the nearby Plaza del Instituto. It regularly screens films, puts on plays and hosts music and other cultural events, and students are frequent participants. You can get there by strolling through the park south of Old Town.