I can't tell you about the men's rooms, but the women's rooms in train stations are pretty basic with mostly Japanese-style toilets and anybody's guess as to whether they will have soap and paper towels. (I always carry a packet of tissues and a small bottle of hand sanitizer, just to be safe.) Cleanliness in the train stations is unpredictable, usually not the best.
If you are out and around in public, your best bets are the toilets in department stores, unless you can wait until your next meal or snack stop, in which case you can use the toilets that most free-standing bars and restaurants have.