Guest house Shinagawa shuku - Best access from Haneda Airport!
It is near Shinagawa Station (10-minutes walk distance), easy access from the airport and perfect connection to the city of Tokyo. Reasonable for backpackers : 3,000 yen per night for dormitory and 3,500 yen for private single. I've heard the staff members are very friendly! You can visit many traditional temples and shrines or enjoy many local shops and traditional Japanese restaurants near by.
It appears on Tripadvisor as well.