I agree about the Diner on 18th St. Be careful walking around the mall late at night as there are not that many people there and it is dark. Are you planning on going to sleep at all or staying up all night?

There are some hostels in the Adams Morgan area where you can get a cheap place to sleep then take the bus to IAD for your KE flight.

Make sure you know where you are going when it is late as with one wrong turn you could end up in a rough area.