The convenience stores that are everywhere (like 7-Elevens) usually have sandwiches you can buy. The two main convenience stores are Lawson Station and Family Mart. These are all over Japan, and you can't help but run into them everywhere.
They usually sell pre-made sandwiches like tuna, or egg-saad, or ham with lettuce & tomato & cheese. Those are all good, but the bread is always white. You could always take the stuff out of the sandwich though.
I'm sure if you look around hard enough, you could find things you can eat, just off the top of my head, it's hard to think of things, because everything I like to eat is always fried, or it's sushi.
They do have Denny's, perhaps they would have a good selection.
