here are some of the places that i have stayed before in taiwan,japan and korea these few years. they are all convenient and among the cheapest accommodations i could find.
TAIWAN
Taipei: Taipei hostel (300NT/ night for dorm room)
http://www.taipeihostel.com/accommodations_three.html
The rooms are pretty clean, near Taipei main station ( can walk or take subway to the station).
Kaoxiong: 乐活玩艺 （350NT/night for dorm room, cheaper rates for longer stays)
http://www.pixnet.net/blog/profile/lohoplayer07
The rooms are clean, the owner is friendly but the location is not super convenient.
Alishan: can't remember cost, please email to check
https://sites.google.com/site/svdalishan/
the accommodation is located within alishan, easy access to attractions within alishan and walkable to train station where you can take the train to see sunrise
JAPAN
Osaka: Hotel Toyo (single room priced at 1600yen)
http://www.hotel-toyo.jp/
recently stayed at this place, clean rooms, free usage of computers, near tsutenkaku, tennoji station. a few subway stops away from umeda and namba
Kyoto: Ikkuu (2500yen for dorm)
http://ikkuu.s2.weblife.me/
One of the best accommodation places ever. The guesthouse was once a teahouse and the furniture and building is beautiful. Gives the old kyoto feel. The place is clean and you can walk to gion from the guesthouse. Owner is also friendly. Cheapest accommodation in kyoto that I could find
Nagoya: Ecohotel nagoya (2000 yen per person for double/triple room)
http://ecohotelnagoya.com/
Provides hotel service for hostel price. Towels, toiletries provided with good wifi. Minutes away from nagoya station.
Tokyo: Asakusa smile (1700 yen for 8 bed mixed dorm)
http://asakusasmile.com/index.php#
Located in Asakusa, clean room with good wifi. Need to climb stairs though :P
KOREA
Seoul: Inside backpackers (16,000 won for dorm)
http://insideseoulhostel.com/
Friendly owners, clean place. Free breakfast provided (you have to cook the eggs though)
Gyeongju: Nabhi guesthouse (17,000 won for dorm)
http://www.nahbiguesthouse.com/
Transportation advice and travel brochures easily available. Clean room with free breakfast provided.
Gyeongju: Sa Rang Chae Guest house ( 15,000 won per person for 4-person family room)
http://www.kjstay.com/content_eng/iboard.cgi
Didn't get to stay at this place because it was fully booked. Saw great reviews online.
Busan: Blue backpackers (20,000 won for dorm room)
http://www.bluebackpackers.com/
Convenient location, easy access to downtown busan, clean rooms with strong wifi
I have personally stayed in all these places and found them to range from so-so to great but they are the cheapest or among the cheapest accommodation I have found. :)
