You might want to take a look at
Superhotels; and the location I am thinking of is the
one near Ueno Station, although there are two near Ikebukuro station
near the West Exit and
North Exit. They do not have "twin rooms" exactly but they do have a set-up for two guests in one room with a "semi-wide double bed" coupled with a bunk bed - with a non-smoking option too.
The prices are slightly above your indicated budget at around Y9.480 per night but you get free breakfast if that is any consolation. The other problem is that their online booking site only handles reservations up to four months in advance; if you email them directly however I am sure they won't mind.
Other business hotels like the
Route Inn and
the b hotels including the one in Ochanomizu were priced beyond your budget.