At TNR Bradford Plumer explains why the mafia never gained a foothold in Washington, DC. Basically his answer comes down to ethnicity: Washington never had the population of Italian-Americans that other cities had and so there was no critical mass for a mafia presence in Washington.
Read the piece to see his answer. I'm a bit surprised that he does not consider one important factor: The mafia has always been only somewhat powerful, though that;s small solace to its victims. Nonetheless, even the Corleaones knew that there was only so far that they could push. You could own a single Senator in Nevada -- and then only under fairly extreme circumstances -- but almost certainly not in Washington, where the power dynamic changes considerably. It is not a particularly effective marshaling of resources to try to play a power game in Washington when New York and Providence and Philly and Boston are so much more wide-open to you.