I lived a lot closer and had friends going last year, plus I was 17, so it was a little easier to talk to my parents about. But, I can give you a few tips that helped me.
1. Look for friends or people from your local field that are going. Then ask if you could tag along and have your parents meet them.
2. Really show them how much it means to you. (get in shape, be on your best behavior) and if they ask why? Say its for LL
3. Make a budget and be very professional while suggesting the trip.
Those are a few thing I did and helped my parents let me go. (But i was driving, not flying) Like PaintballinSL said, they can go on a mini vacation too!
Good luck and I hope to see you there this year man!