I finally couldn't take it any more and bought myself a bike (sorry for the blurred photo, but you get the idea). Not the high-speed tourer I'd like to get—with any luck, if I really budget myself I'll be able to buy one of those in a year or so—but a "mamachari" (from "Momma Chariot", I guess): it'll get me around town, and I can get a little bit of exercise and let off steam after (more likely before) work. And it was only ￥15,000, a little under $150.
Having a bike makes me feel more independent, more able to spend hours searching around the city without wasting money on the trains and without getting blisters. Not so great on the knees, though.
Another nifty result is I had my first contact with people in the neighborhood. The bike shop where I bought the bike is a tiny little place just south of Gotanno station. I talked the owners up a little bit in Japanese, and we parted bowing and smiling—of course, they had sold me something, but that's not the point. I now have a relationship with them, will be able to smile and say good morning when I bicycle by, and will go to them any time I need anything fixed. It's one the steps to widening my circle of relationships. It is important to me to do this to avoid the feeling of alienation I would feel if, two or three months on, I had no familiar faces in the neighborhood.
I rode along the Arakawa river for about 20 miles! I was a little surprised I went that far, and with only one gear.
A final note: one of the nifty things about these mamacharis is they have a light that uses friction against the wheel to generate electricity. It slows the bike down, goes out when the bike stops, and eventually rubs through the wheel, but it's still pretty cool. I haven't used it yet.