I'm doing an exchange like that next year. I happened to talk to the right person about it and they actually ended up setting a program up for me through my school.
I only have begginers Japanese, but I'm studying daily so that I can prep for being there. Be warned, there are quite a few catches. You'll probably have to pay your school fees, find a homestay, buy your uniform (coincidentally if you do find a program, these will probably be covered for you), and do an extra year of high school to get your university pre-reqs.
Start looking around, and talk to your principal, and probably the school board to see what's available. You'd be surprised the amount of stuff that is there, but unadvertised.