I love this idea, but I've struggled with what to replace it with. "Tell me about yourself" is the best thing I've come up with, but it sounds like an interview. "What are you interested in?" is another option, but it too sounds formal. I want to ask people what they care about without having it be awkward. How do you open small talk with someone you've just met?

Good question, but I think the answer is in the question:

  I want to __ask__ people what they __care__ about... 
  How do you open __small talk__ ...

I would make small talk about something small, like the weather (I'm British :), or about whatever common experience around us we're sharing (the music, how bumpy the bus is, how full the flight is). Taking a random walk through conversation-space should fairly quickly get to something that they care about, so long as they want to talk, and have their self-interest-heuristic turned on.

So I don't think you need to seek what they care about. You just need to make the conversation worth continuing and it will get their on its own.

"What do you do for fun?"

"How do you spend your time" is a good alternative. If people are out of work, or hate their job, it doesn't alienate them, yet allows them to talk about it if it is important to them.