A few schools will accept you without an entrance exams (mainly teaching you in English, and teaching you Japanese at the same time), some of which are the International Christian University, Sophia University and Temple university. Temple though, is an American university, with a campus in Japan. I don't know if they will teach you any Japanese at all (unless that's your chosen subject).
It seems you are looking for ryuugaku entrance, which mainly is the same as kikokushijo entrances, which aren't rare, but usually have a limit of maybe a year or two after you graduate highschool, once that time limit has passed you won't be able to apply so don't be sloppy with your application.
Although the exams are easier, there are much fewer spaces available for ryuugaku/kikokushijo entries so competition is high. Although I beleive JLPT isn't a requirement (or atleast not for all the schools), the entrance exams themselves are based on native Japanese entrance exams, you just have to take less test subjects, but you will be scored thoroughly on your Japanese skills, written and reading.
I must say, however, that you shouldn't aim to get into a Japanese university "at all costs". Meaning don't go to a crap university if it will let you in, most companies will look at a graduate from a low-rated uni and laugh in their face (ok I'm exaggerating) but if you don't have a famous uni to your name, it might be better to have a foreign one. Worldwide, Japanese universities aren't too highly ranked either, or so I've heard. I can't say what sort of difference, if at all, studying in Japan as opposed to a foreign country will do for your jobs prospects, but I doubt it will be a huge factor, except learning the language (which you can do outside the country!).
What would I know though, lol, unviersities here won't even take me seriously, hahaha...