Chiming in late to this thread but I had to add my $0.02:
I lived in DC for over 10 years, loved every second of it that I wasn't on Metro, and moved away when my wife and I decided to start a family. Great city, I had the perfect career, but I refused to raise a child there.
This issue isn't crime, or the arts scene/lack thereof, or costs. The issue for us is the poisonous culture of wealth, power, and entitlement from which it is impossible to shield your children.
You may vow never to throw a birthday party that costs as much as a lavish wedding reception and where your kid receives 30+ expensive presents, but your kid will attend 30 parties per year just like that and wonder why you don't love him as much as other parents love their kids.
You may talk a good game about meritocracy, but your kid will watch as her friend's mother pulls strings with a white house staffer to circumvent the intern application process while you preach fruitlessly about playing by the rules.
You may think you need not worry if your 7th grader is going to weekend parties where guys line up outside the bathroom to take their turns kissing, groping, and receiving blow jobs from designated girls, but then you find yourself spending a Friday night walking outside someone's house like a guard at Alcatraz to make sure nobody is getting high in the backyard.
While there are pretty firm lines in the city dividing wealthy whites from the grinding poverty of most of the population, the suburbs are more mixed, with bureaucrats living next door to lobbyists and congressmen. The culture infests every household, and all you can do is accept it or move away.