Large cities often had a hill or high point in the town called the acropolis. This area would be used as a last area of defense if the city was attacked.
Often there were temples to the gods situated around the agora and in the Acropolis. Most cities had a single god called a patron god that the city was dedicated to. They would have a special large area and temple for their patron god.
The dead were not buried inside the town. Typically a cemetery was located somewhere down the road outside the town. Some towns also had a special sanctuary nearby. The sanctuary was a place dedicated to a god where the sick could go to be healed and people would go to hear prophesies about their future.
Many Greek cities had a large open-air theater where plays were held during festivals. Greek theater was a popular form of entertainment. Some theaters were large enough to hold over 10,000 people.
The Greeks also enjoyed sporting events and contests. They built large stadiums (called the stadion) and had gymnasiums. The hippodrome was a stadium designed to hold chariot races.