Asylum has a full vegan menu, although it is unfortunately located on 18th in A-M, which basically rules out going there Friday and Saturday nights. They have a great vegan brunch on Sundays as well, although it's usually pretty packed.
I ate there at least 3 times a week when I unfortunately lived in DC. M'Dawg, across the street, has the best vegan hotdog I've ever had in my life and has tonnes of interesting condiments.