A few minutes by train from Shinjuku is Ikebukuro. I've stayed at the Daiichi Inn Ikebukuro which is right outside near the station.
For the dates you mentioned they have internet specials, they have standard twin rooms (24㎡) for 8700 JPY per night (10,700yen if you include breakfast).
http://www.hankyu-hotel.com/cgi-bin2/cms2/stay.cgi?hid=11diikebukuro&page=room&code=416 (Japanese page)
They also have a smaller studio twin room (16㎡) for 7700 JPY per night.
http://www.hankyu-hotel.com/cgi-bin2/cms2/stay.cgi?hid=11diikebukuro&page=room&code=413 (Japanese page)
There's also an option for an "executive" twin room at 9700JPY per night.
ENGLISH SITE: RESERVATIONS:
http://www.hankyu-hotel.com/hotels/11diikebukuro/index_en.html
I've stayed there before, it is a nice small business hotel, even though it is near the train tracks I didn't have trouble sleeping.
Edited: 10 years ago