If you can read Japanese well enough to use the Japanese travel sites, you will find that their on-line reservation forms won't handle international addresses.
The sites below work with lodgings that are willing make the extra effort it takes to host international customers. As you know, we foreigners can be hard to communicate with and tend to rely on our hosts for more assistance (e.g. Where's the nearest coin laundry? Can you help me fill out this form? What are the hours for such and such a park?)
These are the sites I like:
Welcome Inns - http://www.itcj.jp/eng/index.php
This site is good especially if you want to stay in a Japanese style inn, sleeping on a futon in a tatami room. Some have meals available and they are usually really good. Prices are reasonable, too. The way Welcome Inns works is that they contact the lodging for you. They will then contact you by email with a confirmation number. If the exact dates or room type you want are not available, they may suggest an alternative and give you an opportunity to accept it.
Rakuten - http://travel.rakuten.co.jp/en/index.html
Although this site has a some Japanese style inns, their strength is in the number of listings of reasonably priced business hotels. Although business hotels offer only small western-style rooms and don't usually serve meals, they can be located very conveniently. It's good to be near a transportation hub so you can get to all tourist attractions easily. With many of the hotels on this site, be prepared to pre-pay for your stay. I rather like pre-payment, because I know that even if I lose my wallet, I've got a place to stay.
JNTO - http://www.jnto.go.jp/a-search/search/search_form.php
The Japanese National Travel Organization points to lots of other lodging reservation sites. I would trust site listed by the JNTO.