Alexandria is as safe for kids as the other areas, except it's more urban and therefore more worries about them riding their bikes /crossing the streets than in a subdivision cul-de-sac.
Old Town Alexandria still has some public housing (not as much as in past) where you might not want to walk through at night or park your car, but you don't have to be in those areas. I live near some of them and I've never had any problems, but there have been a few muggings I hear about in the local papers. Arlandria along Mt Vernon Ave has the bulk of the crime statistics. Arlandria is not the western end of Alexandria, it's the northern-most part along Four Mile Run, just at the Arlington county line and heavily Latino. West End refers to the Duke St (Rt 236) corridor up to Landmark Mall, and areas around Seminary. Cameron Station is the more recent "nice" part of West End.
Housing in Alexandria City is typically more expensive than the Fairfax County areas you've mentioned, and less living space. Most Fairfax County schools are higher-rated than Alexandria schools, also. But Alexandria is more a real town, and not sprawl like Fairfax County is.
I don't know about the bus availability in Fairfax County as it's been years since I've lived there, but if you choose a place without bus service to Metrorail, be aware that Metrorail lots can fill up quickly on weekdays. Burke is the furthest out of those you mention, and is more green and country-like, I suppose, than Springfield or Annandale (still lots of traffic, though - just not a glut of strip malls).
I second the idea of looking at Falls Church.