cavea
Τhe auditorium or audience sitting of a theater.

proedria
It was the right to sit in the front, especially made, seats of the theatre and it was applied to priests and magistrates of a city as well as to official envoys of other cities. In addition, this right was bestowed to people honoured by a city.

scene (lat. scaena -ae)
The stage building of the ancient theaters originally used for storage but provided a convenient backing for performances.