I understand, I think. The question is, as a woman alone, is there anything specific one ought to know about eating out, going out, being in places alone, etc.?
Yes.
1. Before you eat at a restaurant of any kind, at an ordinary meal-time, just look inside a bit — a quick glance through the window or a briefly-opened door will do it. Here are your questions: How thick is the smoke? Are there any women? If so, are they young, smoking, dressed “hot,” and with men?
If there’s minimal or no smoking, go ahead.
If there are middle-aged women, go ahead.
If there are women of any age sitting with one another, go ahead.
If the air is thick with smoke and the only women are young, smoking, dressed for “action,” and with men, give it a pass.
Not that anything will happen, probably, but the atmosphere is not going to be super-comfortable. This is a bar-restaurant aimed at men and/or women who (at the moment) want to appear a bit wild.
2. At lunchtime, restaurants divide into three groups: male, female, and mixed. Male means guys bolting ramen and running. Female means OLs (office ladies) or groups of non-working (at the moment, anyway) women having a fun lunch together. Mixed means a family restaurant. If you want good food, go for female: the salary men don’t care. If you’re starving, it doesn’t matter, but a family restaurant will probably be more comfortable. Every terrific lunch at a non-super-expensive place I have had here has been at a place where I am pretty much the only male customer.
3. The thing to watch out for is trains. If on a crowded long-distance train, there is probably a “ladies only” car. Use it. For some reason salary men on trains lose their marbles and grope women appallingly. It’s one of the most disgusting phenomena in Japan, actually, so don’t be on the receiving end. Outside of approximate rush hours, especially evening commutes out to the suburbs, it’s not likely to happen, but keep a wary eye out for guys in suits moving toward you in a creepy way. Rape is extremely unlikely, but I doubt very much that you want to be mauled around.
In general, I’d say this country is an excellent place for a woman to explore on her own. You might want to keep your question in mind as you travel, though, and see whether you spot some of the subtler ways in which discrimination occurs: quite interestingly different from home (wherever home is).