Where does the play open?

Act I, scene 1 of Twelfth Night opens at Duke's palace in the kingdom of Illyria, with Curio, other attendants, and musicians waiting on Orsino, the Duke of Illyria. As many scholars have noted, Illyria is a land, perhaps a little like Belmont in The Merchant of Venice, that is a characterized by romance, along with what Shakespeare scholar David Bevington calls a "carnival atmosphere," (which indicates norms are going be turned upside down) and sensual pleasure.
Romance is a predominant theme in the opening scene, as the Duke pines with unrequited love for Olivia, a woman who, in this somewhat whacky world, is planning to shut herself up in convent-like mourning for seven years. Sensual pleasures are a part of this first scene, in which Orsino has his musicians play for him to help him cope with his unrequited love for Olivia. Establishing a sensual atmosphere from the start, the Duke asks for a "surfeit" of music. He says that if music be the "food," or fuel, of love, he wants so much music that he will get sick of it and therefore get sick of love itself.
The opening scene very much sets the tone and mood for the gender-bending romantic comedy that will follow. This duke seems not a bit interested in politics or warfare—he is only interested in love.
Illyria itself was far from England, on the Adriatic sea—a good location for a shipwreck.

William Shakespeare's Twelfth Night begins with a shipwreck on a desolate and foreboding jagged coastline. Geographically, the story opens on the coast of the Adriatic Sea, which was once called Illyria. This was the name given in ancient times to that specific region along the Adriatic coast, which today consists of the countries Bosnia, Albania, Croatia, Serbia, Slovenia, and Montenegro. Other locations at the beginning of the play—which is also where the majority of the story is set—are Duke Orsino's palace, Olivia's house, and the adjoining gardens. All of these locations are in and around Illyria. William Shakespeare decided to open Twelfth Night, as well as set the rest of the narrative there, because the name sounded exotic to the English crowds who watched his plays.