Dating from 80 BC, the massive Amphitheater at the far end of Pompeii, which seated 12,000 spectators, is the oldest surviving Roman amphitheater. 

Right next to it is the Palaestra, with colonnades around three sides and a swimming pool in the center. 

Beyond the Porta di Nocera, outside the city walls, is a necropolis (cemetery), much like those that lay outside the walls of all Roman (and other) ancient towns.