I taught at a NYC school, and had the opportunity to see these schools in action at Manhattan and at Feds, and it really is impressive and fun to watch programs that have such history and tradition, and such high expectations from their runners. In large part I suspect that the tradition is self-sustaining to an extent (as long as the quality coach or qualified replacement is guiding things). There is obviously some very excellent coaching going on upstate. In this day and age of dyestat and NXN live on the internet, and Footlocker champs on cable tv and streamed live as well, the successful programs can feed off previous success to attract better athletes and really make cross-country something attractive to prospective runners. It was one thing to say that Mark bloom in the Harrier magazine that maybe 250 people read said that we were national champs... it's a whole nother thing to be flown out by Nike, showered with cool swag, rub shoulders with olympians, and have your fans watch the race live on tv.
So, i think that tradition is a big reason. But why New York? (the question of why girls rather than boys has already been answered and quite clearly has to do with the lack of depth of talent on the girls side). As much as they seem crazy to me, I think you have to give a lot of the credit to the Kranicks who run the Saratoga program. I remember in thes stone age pre-dyestat days of the mid 90's when i ran xc in college in new england, i first heard the stories of the cross-country dynasty down in Saratoga. I don't know how many straight years they won Feds or were crowned national champs by Bloom, but it was something absolutely out of this world. I think that they really set the standard up there before the explosion of running on the internet. Other schools were forced to compete with them at the sectional level (shenendoah) or feds level (burnt hills, hilton, etc...) and that raised the level of everyone in the area and the state (or at least any team with designs on a state championship). Thus New York was uniquely prepared to compete at the national level when NXN started. Plus, that first year was the incredible mixed Greenwich-Saratoga "team" that put 4 girls in Foot locker finals. These teams were used to competing and just as importantly training at a supremely high level, and that shows in the results. I suspect as the years go on this initial advantage will wane (also as the depth in girls running gets better), but it is a super-strong tradition and I suspect New York teams will always be in the hunt.
all the other stuff - rich families, or poor families, good work ethic, bad weather -- none of that is specific just to the area. The tradition and competition that dates back to the Saratoga dynasty days is.