Actually, questions regarding one's home country would often trigger positive feelings.
Most people like to share their culture and are very proud of their own country. Ask them a question that would allow them to share more of their own hometown/city, and they would more than willingly oblige to speaking about it.
Rather than asking personal questions, ask things about what they've seen, and how different is their country like from yours.
Questions such as:
"So what is your country like? Is it very tourist-friendly?"