Not when their parent's music is punk rock. There is no further rebelling.
Me, I liked to listen to jazz, which my parents didn't really like. My dad's learned to like it, like I've learned to appreciate Gordon Lightfoot, but it's just not his music.
Now my grandfather listened to pretty much nothing but swing music, which I've always liked and was cool for about ten minutes in the 1990s when every eager young hipster started dressing like me and listening to swing music.
Yep. I look like a Gap ad from 1997.
Okay, to address the actual topic of this thread:
I like mix discs (minidiscs, usually) when travelling - my latest includes some new tunes from Belle & Sebestian, the new Strokes album (which isn't all that great), the Kill Bill soundtrack, the Postal Service, New Order, the Smiths, Elvis, Elvis Costello, Public Image Ltd., the Pixies, Fiona Apple, Dave Matthews Band (sometimes it's just "Lover Lay Down" on repeat for a half an hour), Sparks, Tori Amos, Bad Religion, Fear of Pop, Morphine, Soul Coughing (always good driving music), They Might Be Giants, Meat Beat Manifesto, Nirvana, Ned's Atomic Dustbin, EMF, and Sade (although I prefer the Marquis de Sade).
I highly recommend the new Belle & Sebastian album "Dear Catastrophe Waitress" which, while a bit twee, is funny and has a nice 60s swagger to it. And VERY VERY Scottish.