Depends what you want. If you have 2 people then a 2窶喞K is prolly what you want, a 2 room, with dining room and kitchen, and normally has a bathroom and toilet. Not very big mind you.
As for the cost of something like this theres some factors, location being the key. Where? And then again where?
Example - in Tokyo? Right, now how close to tokyo? Right, now how close to a train station?
An apartment out of Tokyo next to a station wont always be cheaper than an apartment close to Tokyo but nowhere near a station.
So lets see, Kita-ku where I lived for a while is on the norther edge of Tokyo, about 30mins from everything, a good location. Generally its got stations, both JR and subway everywhere, so your looking at anything from like 60,000-110,000 yen a month. But then theres bond and key money... 10,000-20,000 for 窶氾ｧ窶ｹﾃ? (key money) which you'll never see again. And around the same, sometimes less for 窶｢~窶ｹﾃ? (bond) which is like a safety deposit, be a good tenant and theres a chance you'll get it back.
I like this site, but without Japanese it can be a little tricky -
【CHINTAI】賃貸マンション・賃貸アパート・賃貸物件など不動産賃貸・お部屋探し検索サイト｜スマホで賃貸
What do you need housing for? Short-term? Long-term? Planning to work? Holiday? Theres better ways then renting, especially in Japan....