Although not a frequenter of hostels, I was pleasantly surprised by Duo Housing. The house is very clean, due to the stringent rules about shoes and food. The rules in place are necessary and appreciated, but don't break any of them. We accidentally entered the kitchen during the Sunday dinner and got yelled at by the owner/manager.
We stayed on bunk beds in a 12-person co-ed room. There are four rooms, all co-ed, and the hostel can house 58 people. Duo provides linens and towels and free breakfasts every morning. The pancakes and coffee are mediocre, but the Sunday night dinner was very good and had a large variety of options. The location is about a 20 minute walk from the edge of the Mall and 5 minutes from the Mt. Vernon Sq metro stop. It's pretty convenient but not close enough to come and go very often throughout the day.
Security seemed fine. I felt comfortable leaving my luggage there during the day, even after checking out. Bring a lock to put your valuables away -- the lockers are big enough for a few laptops and documents. Our main complaint was the staff. The woman who checked us in and gave us a tour was very welcoming and nice. But the rest of the staff were awkward and did not go out of their way to be social. The owner/manager was curt and seemed very strict about his rules. Just don't cross him, and you'll have a very pleasant stay.