I would check with the individual language schools for age restrictions, but I don't think it would be an issue. I attended a language school in Beijing in my 20's and there were students of all ages there.
The real question should be what are your goals? Do you want an intensive program to quickly acquire language skills, possibly for seeking employment afterwards, or are you just hoping for an excuse to get a student visa and enjoy some time in Japan?
If you're serious about language studies, I'd go with a school like:
The Naganuma School