Hope you plan to do a more thorough investigation than just relying on a greatschools rating. Go and visit the schools, and attend a few events like science fairs and plays.
That said Croton has excellent schools. They are arguably the best in Northern Westchester, and are consistenlty ranked among the best in the country; still though, usually a notch below Scarsdale or Chappaqua. (see link below)
Two Cortlandt Schools Ranked With Country's Best | The Croton Daily Voice
The demographics of the parents is more diverse in Croton than in Scarsdale or Chappaqua in terms of the perecentage of residents with post graduate and ivy league degrees. The fact that Croton schools consistenlty rank just a notch below them is quite remarkable taking this into account. In Croton your child will have classmates whose parents' professions range from medical doctors and software engineers to firefighters and Amtrak employees.
I'm assuming that the reason you can't find a "suitable" home in Scardale or Chappaqua is because you can't afford to purchase a "suitable" home in one of these places. If this is the case, than you and your child may also find yourselves socially isolated if you can't afford to be a member of a local swim club or country club.
You won't have this problem in Croton. All residents share and equally enjoy the villages wonderful parks, resources, and great schools.