I received an email tipping off to the existence of a new hostel called DC Lofty. It's located just off H Street. You could easily miss it because there is no sign out front. But they do have a website with photos.
From the website-
Our address is 815 7th st, NE Washington DC 20002. It's one of the nicest areas in Washington DC, with an H street mall and a library less than one block away, and the metro 10 minute walk away, about 5 blocks.
Our location is less than a block away from a large mall, with all your shopping needs.
They should totally have played up the free WiFi at the carryout McDonald's.