"food in the housing market"? how great is this expression?! :)
400 leva in the city centre - well, just forget it - 600 leva is a more reasonable starter price - we are talking about furnished appartments, of course.
I would not recommend Lozenetz or Vitosha - traffic in Sofia is horrible - they would spend hours in the car. And besides, what car? I assume that they won't drive... Public transportation... well, you know pretty well. However, they could still choose something in Mladost that is near the metro station