There are many monthly "mansions" for shorter stay. The listings I found in TYO metro areas go from at least JPY 100,000 per month. I am now living in one of those mansions in Shinagawa until the end of this month when I move in a place in the Chofu areas as my primary residence. The short term mansion comes with the basic amenity for the normal daily living (refrigerator, microwave, washer, air conditioner, mail box, and etc). It is very convenient as a way to set up a living while you are looking for a longer term residence.
Typically, if you rent more than 3 months, the montly rate can go down.