The higher-ups traditionally get the better gifts. Alcohol, consumed in mass quantities by the male population here, is also appreciated, although there are strict limits as to what you can bring in through Narita International Airport. Read the Yomiuri English newspaper over breakfast. Teachers go over the days business. I am at a base school, which is different from most of the other JETS around me.
Many JETS visit quite a few different schools during their year.
Although as the program size has been increasing, the number of school visits has been declining. As far as your school schedule goes, it will be decided for you, and at first you will probably have very little say about it. Some JETS take second jobs during the evening, usually teaching English privately. Although this is forbidden in your contract, if you live in a big enough city and can get away with it, it is a good way to make contacts outside of work and pick up some extra cash. I end up going to Tokyo on the weekends, just because it is so close.