The Art of Problem Solving (AoPS) website is an extraordinarily rich source of online lectures, books, and forums. Some books and lectures are content-specific (e.g. Geometry, Precalculus, etc.) and others are contest-specific, with courses directed to the AMC-8, 10, and 12, the AIME, and the USAMO. Prices are reasonable, and the range of opportunities is enormous.
Westchester Area Math Circle offers opportunities for math students of all levels and abilities. It meets at Manhattanville College and holds classes on Wednesday afternoons (a beginners’ class and recreational math class), and has a meeting on Sundays for students interested in advanced math contests. They enter a team for high-level math competitions. For more information please see their website, or contact Paul Ellis at paulellis@paulellis.org.
New York Math Circle meets at locations in Manhattan and Brooklyn and provides excellent opportunities for enhancing your math and problem-solving ability.