"Los Angeles is a city in the United States. In California to be more specific." Then, after a moment of consideration, "A drag competition is..." She sighed softly. "Gay men who dress up as women are considered Drag Queens, for the most part. I am a Drag Queen. I was going to a competition with a few of my friends. In Los Angeles."
It wasn't that she was trying to hide who she was, she just wasn't exactly sure how to explain it to someone from 1500 years in the past. Without confusing the poor man even more.
"I would be willing to share my apartment, if you would be okay with that. It has to be better than living in a tree."