This is a rare, truly budget option in Shinjuku, just blocks from the neighbourhood's nightlife (but in a location that allows you to avoid passing through the red-light district, Kabukichō). Of course Imano is going to attract party people, so give it a pass if you prefer a quiet night in. The bunks are simple, with privacy curtains; staff are friendly and speak English.
There's one 'family room' that sleeps up to five (from ¥20,000)