The list below is good but from personal experience nothing compares to the Seed. The staff is wonderful and caring and the education your child will receive is second to none. My daughter went there for 1 year and I was sorry I didn't find it earlier. She absolutely loved it.
Do your research on the Goddard School of Yorktown Heights. The NY State Office of Child and Family Services has issued Goddard School of Yorktown Heights 7 violations in very recent months for inadequate supervision of children in its care, along with issues that relate to safety and welfare of children in its care. Go to the NY State Office's website to read the facts (not an opinion): http://it.ocfs.ny.gov/DayCareFacilitySearch/Profile/Index/457604
Depending on where you live in Eastchester, if it is convenient for you, I sent my children to Hitchcock Playcare in Scarsdale, when they were they were 2, and then to Hitchcock Weekday School when they were 3 and 4. It is held at the Hitchcock Presbyterian Church, but is not a Presbyterian school. My girls were very happy there.