There is a new program called PRIMES for high school students in the Boston area. There are lots of high school math programs out there, but this one is fairly unique in offering a research experience. (RSI is the only one I know of, and PRIMES is based on it.) Also, unlike most of the others, it is during the school year as well–that’s why it’s only for kids in Boston.
Anyway, it looks like a very nice idea, and the mentor-in-charge, Pavel Etingof, has a fair bit of experience with this sort of thing. So if you’re a high school student in the area, apply! Or if you know one, tell them about it.