I run after dark in NW multiple times per week for the last 4 years. It's safe, never had any issues. Just stick to busier / better lit areas if you can. And be visible, getting hit by a car is a much bigger threat than getting attacked or something imo.

I mainly run down 16th st between silver spring and Dupont, which has plenty of street lights and usually some other people out. I also sometimes go down past the white house and around the mall / reflecting pool, which is obviously super safe. Guaranteed you'll see other runners down there.

I never run with headphones out of personal preference, but its certainly safer that way also. I also sometimes clip a small blinking light on my chest to make myself more visible to oncoming cars so they don't right turn into me as I'm crossing an intersection (I usually run on the left sidewalk against the flow of traffic).