Corinth, Greece, in front of Jason and Medea's house
Medea is set in a city-state called Corinth. It's interesting that, though most Greek tragedians lived in Athens, their plays are hardly ever set there. In fact, they weren't allowed to do so. Guess it just hit to close to home. The tragedies did almost always examine issues that Athens was currently wrestling with. However, Athenians seemed to have preferred a little objective distance when thinking about their problems.
Athenians also seemed to dig objective distance in terms of time. Tragedies were almost always set back in the day, somewhere in Greece's distant mythical past. Euripides and his fellow tragedians drew from their culture's rich tradition of heroes and gods to weave their tales. Jason and Medea are great examples of this.
More specifically, the play is set in front of Jason and Medea's house. This seems quite appropriate. It's a tragedy that shows the bloody dissolution of a family. What better place to set the play than in front of the house in which the family once thrived? It's ironic that this place that once gave them shelter is now the setting for mutually assured destruction.