Yeah, I don't really know what you're interested in, so I just listed a bunch of stuff I think is cool.
As for work and school, they will assume that you spend at least 3-4 hours doing homework every day. Expect a few hundred words + kanji every week if you study at a higher level than total noob.
I never experienced any discrimination or bad treatment during my year there, but of course some people may stare and/or mutter to themselves if they feel you're in the wrong place, but that's their problem. That's mostly old farts anyway. Even if they would have a problem, they won't say anything. IF you do see some place that doesn't allow foreigners, you probably wouldn't want to go there anyway. Mob owned places etc.
But tattoos of any kind are absolutely forbidden in most baths, yeah.
I guess there are rail passes, but I don't it's worth it if you won't do a lot of traveling around. The best thing is generally to just buy a pasmo/suica card and load it with money when needed. They work on all JR lines, and most others(subway) too. I heard you can set a card to work just between two stations and get a rebate, for work/school commuters.