Having worked in a number of research labs, I would add to this that you should also try contacting professors at the nearest college. Very rarely is there something structured put in place for high school students to work at universities, but that said, many professors will work around/through/over the bureaucracy so that you can work with them. Often times all that is needed is a bit of initiative and some personal contact.

In other words, if there's one thing I've learned so far in life, it's not to underestimate the power of simple human contact. Go knock on a random professor's door, and I think you'd be surprised how many times the door opens!