Rich kids from the tri-state equal diversity?? A smart kid will excel and shine in any district. Having the opportunity to take AP classes in HS is huge; it can help gain admission to the super selective, as well as save money on tuition. Achieving honors in prestigious competitions can be a stepping stone into highly sought after placements in college research labs. Take districts such as Jericho, Cold Spring Harbor, and Commack, look at their statistics and you will see that the real facts don't lie. Public can be just as good, if not better than private. You are lucky that the private schools are only taking the brightest, that way when they have uncertified teachers teaching their classes, they will be able to learn on their own.
Taking AP courses in High School is not enough to stamp yourself as worthy of Top 40 institutions. Taking the most rigorous courses available at your High School is a baseline requirement with performance in those courses and so many other factors contributing to the final acceptance. However, you are correct that Advanced Placement does contribute heavily.
Another point to remember is that while courses can be waived (for example, a "4" or "5" on the Calculus BC exam will often waive first and second semester College Calculus), you will need to check with the individual school regarding credits in residence requirements; in other words, do the credits awarded count to the number needed for the degree or just do they just waive the need to take a given course?
Also note that some school districts (Commack for example) do not typically follow an AP Curriculum, but license the International Baccalaureate (IB) system. Lesser known than the AP Program, IB offers similar course work with a slightly different focus on writing skills.
