Upvote:2
The key word for medium-term rentals in Japan is "weekly mansion", search for that on Google and you'll find a whole bunch of sites offering them in English.
That said, your expectation is not very realistic, as less than US$300/Y30k a month in any of Japan's major cities will be virtually impossible. You'd generally be looking at Y50k and up for some tiny shoebox in an inconvenient location (and when I say tiny, I mean tiny, there are apartments in Japan under 10 sq.m.!), and even doubling that won't get you very far.
Upvote:3
As for Tokyo area, check out http://www.sakura-house.com/en/
Depends on where you are planning to go, dormitory style may get you down around $500. If you are interested in another area, you might ask them for a referral. Possibly it could be less outside of major cities.
Also you can search on Google for "japan apartments "no key money"". In Japan, normal apartment renting for short term is not practical, because you have to pay traditional key money and various fees, in addition to rent.
Upvote:3
I have staid for in Seoul (ROK) a few months in 2009/20. The cheapest option was to take a roomlet in a 'gosiwon'. The room was 5 sqm, (2m wide, 2m long + a 2 * 0.5m bathroom). for ~400k Won a month
Rooms included TV, Broadband internet, a small fridge, a bed (60cm wide, 2m long), a few cupboards and shelves.
some info might be found here: http://www.habang.co.kr/b_go_se_en
Upvote:4
Have you tried airbnb.com ? It is possible to find some very good deals and have reviews of people that stayed in that place (just like hostels.com or other sites).