The short and long answer is that it doesn't matter. If Japanese people ask you where you're from, the only answer 99% of them are going to understand (and want to hear) is really just "America." Some of them know the difference between New York and Washington - or at least that there is a difference, and it mainly has to do with where Ichiro plays baseball; but let's face it, when you're talking about a country on the other side of the world, that's about as detailed as it gets outside of geography class. I don't mean to say that Japanese people are especially unworldly. If a Chinese person told me their hometown, I think I'd be in the same situation! I know where Hong Kong is, that it was once ruled by the British, and I know that Beijing is somewhere to the northeast of it and had the Olympics. Not much else. God help me if a Chinese person is from an interior province.
The difference here is that you can at least educate, or entertain, with pictures, clothing, foods, music, and other things that represent where you are from - note I don't say "where you were born" or "where you grew up." If it feels like a lie, then ask yourself who is going to know (or care)? I used a picture in my self-introduction lesson of a family friend and called him my uncle, just because the JTE asked for a picture of my family and I wanted to show a picture of an American barbeque (it was the only picture I had of somebody grilling).
Some of these pictures will come in handy for your self-introduction lesson, others may just come in handy in talking with other teachers about where you're from. I'm from a small Midwest suburb, but I spent a lot of time living in the Rocky Mountains, in various cities for college and work. In any case, most of my pictures are from hiking trips I've taken in the Rockies, so when I tell other teachers where I'm from and use pictures to show, it usually ends up being a photo collage of places from all over the Rocky Mountain region.