The dollar hasn't been doing well against the yen with the recent economic trouble but in my experience Japan is relatively okay for accommodation and Tokyo is not that much different from any other major international city.
The big hotels are going to be over 10,000 yen (about 112 US/140 Canadian dollars right now) but I stayed with some friends in the Star Hotel
for about 13,000 (about five years ago mind). That wasn't bad split between three people in a triple room. Looks like their prices haven't changed much.
You can get a business hotel for around 6000 - 7000 yen (67 - 78 USD). This one in the heart of Shinjuku is 6500 for a single (5% off if you reserve by internet): http://www.annexh.jp/
There are some more on google map
but if price really is a problem you could look outside Shinjuku. It's easy enough to commute. Ryokans (traditional Japanese Inns) in the region seem to be around the same price although most of the ones I've seen in Shinjuku look more like business hotels anyway.
For a really tight budget there are capsule hotels for about twenty bucks: Although I have stayed in relatively comfortable capsules, the one I once used in Kabuki-cho (not too far from Aikikai Hombu) didn't have as much insulation and was a bit noisy.
On an absolute shoestring, try this: Quite a lot of young people just find a cybercafé, pay the 1000 yen or so for a "night package" and instead of spending the night surfing the net while drinking coffee, you can use the comfy armchair (they usually are comfy) to sleep.
Also, if you're desperate you could check out the Lonely Planet guide.
Hope that helps