This year brings with it a new crop of standout schools city families can consider.

I had always assumed my daughter, Meg, would be just like my boy, who was smart and funny, athletic and popular. He fit in wherever he went. I was realistic enough to figure theyd have their own interests, but assumed they would fundamentally live the same life.

In New York City, it’s not uncommon to hear parents with infants—and even soon-to-be first-time parents—talk about applying to nursery schools. There are a lot of anxious questions in the air.