Nevertheless, it's 2013 people are to concerned with security and threat, I would be nervous to bring a stranger into my home I'm not familiar with let alone a family allowing this kind of hospitality would be strange but that's just my opinion.
As for hospitality, people always seem to enjoy something/someone new in their daily lives - as long as you're friendly and don't overstay your welcome, you'll always find someone to show you the city and give you a place to crash for a few days.
Westerners (esp. Americans) are a curiosity and don't seem threatening at all (what with the smiles and politeness) - no Hungarian, Bulgarian or Turk will ever think you're a threat when you're alone and they've got a whole neighborhood to back them :-D.