Private rooms in Tokyo mostly fall in the ¥40,000–59,000 range: above ¥60,000 closer to the centre, and around ¥40,000 in the eastern and northern downtown zones. Compare the monthly total, which is rent plus the common fee (utilities and internet, typically in the ¥10,000s). Sort by cheapest private room to see everything within your budget at once.
Initial costs are usually three items: a deposit settled when you move out, an administration fee and the first month's rent. There is no agency fee as with regular apartments. Houses running campaigns may offer a free first month or discounted fees. Before signing, check the minimum stay and whether a cleaning fee applies on move-out.