Almost all the advice I was planning to offer has already been covered here, but on the gift-wrapping front it can be a problem going through (US) security with wrapped packages. I don’t think they’re actually prohibited, but if TSA has to inspect the gifts then they will open them: http://www.tsa.gov/311/311-holiday.shtm
So while the Japanese will be expecting gifts to be wrapped, it may be wiser to either buy wrapping paper and ribbons after arriving in Japan or cut some wrapping paper before you go and bring it with you.