Optional things to consider

1. Allows Internet or cable TV
2. Airconditioner
3. Last Train... time of
4. Place for washing machine inside room
5. Parking
6. Pets
7. Friends Staying over

There are other minor things to consider. Check to see if the place allows Internet or cable TV (some don't), a place for washing machine inside the room, parking, balcony, pets, friends Staying over and landlord living in the same building. If the landlord lives in the same building, it sometimes gets tricky having guests over or making too much noise... even on your birthday.

One additional thing to consider is what time does the last train leave from major entertainment districts such as Shinjuku, Shibuya and Roppongi. Some days you might want an early night home and not have to take the expensive taxis.