There's a handful of universities in Japan that has some kind of International Department or a department whose classes are taught in English with the exception of a foreign language. The schools I'm applying to are Sophia University and Waseda University, both located in Tokyo and they both have those kinds of departments.
There's also the G30 schools, which are schools that are part of a program to promote international studies and students. Since you're already looking at schools in Nagoya, another school that's in the very general area is University of Osaka. Other colleges in the G30 program can be found at:
About jump (global30) | Study abroad programs offered by leading Japanese universities | Jump.
If you want to apply for the entry of 2012 you should start asking for applications ASAP! I had to email Sophia University to request them to send me their application and deadlines for my school are in December and January! It's a pain to get everything together and not an easy process compared to the Common App for American schools.