Coming in late but another vote for the Aeropress. I used one in my office years back when I didn't really have anything to speak of to clean stuff. I used paper towels (raided the men's room for a stack of them) to wipe my coffee cup out every day, and wipe the Aeropress out after each use. At the end of the week I took both home to be properly cleaned.
It's easy to use, doesn't take up a lot of space, is easy as anything to clean and doesn't generate much rubbish to get rid of along the way.