Illryia is an actual location, found in the Adriatic coast of Italy. (For Shakespeare, the placement of his romantic comedy in this exotic locale had much to do with the audiences of his day. Those theatre-goers "liked to project themselves into the world of romance" as well as indulge in a "nostaglia for by-gone days." Not much has changed about human nature, has it? We still long for unfamiliar beauty, still pine for a the "good old days."
If you think about it, the warm Italian breezes must have been quite appealing to those in the comparatively dim, rainy, and grey weather of England. And chivalry? That most by-gone of by-gone eras, even by the 1500s? Well, many then, as now, cherish the thought of its renewal, at least for a few hours of escapism.
Shakespeare, Wiliam. ed. Bruce R. Smith Twelfth Night. Bedford-St. Martin UP. Boston: 20001.